The authors thank Xiangyu Gong, Xin Wang, and Tong Xu for capable research assistance; Jing Wu for sharing

data on China’s housing prices; and Suqin Ge and Dennis Tao Yang for sharing data on China’s real wage rate.

Thank you to Toni Braun, Satyajit Chatterjee, YiLi Chien, Carlos Garriga, Lee Ohanian, B. Ravikumar, Richard

Rogerson, Manuel Santos, Zheng Song, Kjetil Storesletten, Gian Luca Violante, Yikai Wang, Tao Zha, and the

participants of Brown Bag Seminar at the Federal Reserve Bank of St. Louis; 2013 Tsinghua Macro Workshop;

2013 Shanghai Macro Workshop; 2014 Spring Housing-Urban-Labor-Macro (HULM) conference; and the 2014

Northwestern-SAIF Conference in Macroeconomic Policies and Business Cycles for helpful comments. The views

expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal

Reserve System. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Kaiji Chen, Economics Department, Emory University, and

Research Department of Federal Reserve Bank of Atlanta, Rich Memorial Building, Room 306,

Atlanta, Georgia 30322-2240, 404-727-2944, kaiji.chen@emory.edu or Yi Wen, School of Economics and

Management, Tsinghua University, and Research Division, Federal Reserve Bank of St. Louis, Research Division,

Federal Reserve Bank of St. Louis, P.O. Box 442, St. Louis, MO 63166-0442, 314-444-8559, yi.wen@stls.frb.org

CQER Working Papers from the Federal Reserve Bank of Atlanta are available online at

https://www.frbatlanta.org/cqer/publications/workingpapers.aspx. Subscribe online to receive email notifications about

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Center for Quantitative Economic Research WORKING PAPER SERIES

FEDERAL RESERVE BANK of ATLANTA

The Great Housing Boom of China

Kaiji Chen and Yi Wen

CQER Working Paper 15-03

November 2015

Abstract: China’s housing prices have been growing nearly twice as fast as national income in

the past decade despite (1) a phenomenal rate of return to capital and (2) an alarmingly high

vacancy rate. This paper interprets such a prolonged paradoxical housing boom as a rational

bubble that emerges naturally from China’s large-scale economic transition, featuring an

exceptionally high rate of return to capital driven by massive resource reallocation. Because such

primarily resource-reallocation-driven high capital returns are not sustainable in the long run,

expectations of high future demand for alternative stores of value can induce even the currently

most productive agents to speculate in the housing market, even if housing provides no rents or

utilities. We show that such speculative investment behavior can create a self-fulfilling housing

bubble that grows much faster than the national income during an economic transition, thus

explaining China’s massive “ghost apartment” phenomenon and decade-long faster-than-income

growth in housing prices despite high capital returns.

JEL classification: E22, E23, O11, O16, P23, P24, R31

Key words: housing bubble, resource misallocation, Chinese economy, development, economic

transition

1 Introduction

Housing prices in China have experienced prolonged and rapid growth in the recent decade,

increasing significantly faster than China’s spectacular aggregate income. Data based on 35

major Chinese cities show that average real housing prices have grown at an annual rate

of around 17% for the past decade, far exceeding the nation’s 10% average gross domestic

product (GDP) growth in the same period.1 Closely associated with such a housing boom

is the growing number of empty or “ghost”apartments across Chinese cities. In 2013 the

national urban housing vacancy rate reached 22.4%, far above the level of developed countries

(e.g., the homeowner vacancy rate in the United States was only about 3% during the peak

of the U.S. housing bubble around 2006). Of note, the majority of the ghost apartments are

sold properties, which suggests an excessively strong (speculative) demand rather than an

excess supply.2

During the same period, China has also enjoyed a phenomenal rate of return to capi-

tal. For example, between 1998 and 2012, China’s real rate of return to capital was con-

stantly around 20% or above. This rate of return is unprecedented even compared with

the best-performing emerging economies. Yet housing investors in China consist not only

of middle-income and high-income households but also firms, including the most productive

and profitable firms.

The combination of these features– namely, (i) the decade-long faster-than-income growth

of real housing prices, (ii) the exceptionally high vacancy rate, and (iii) the unprecedented

high rate of return to capital– is puzzling. A standard neoclassical model, either with land

as a production factor or with housing services in the utility function, predicts that housing

prices can grow at most as fast as aggregate income and thus can hardly explain China’s

phenomenal housing price growth and the alarmingly high vacancy rate. Alternatively, in

the classical Samuelson-Tirole bubble economies, housing assets can serve as a store of value

even if they provide no utilities. This framework can explain the massive ghost apartment

phenomenon in China, but it requires the critical assumption that the rate of return to cap-

ital is excessively low in the economy, which seems at odds with the prolonged high rate ofreturn to capital in China.

1The average income growth rate for the 35 largest cities was 11% during that period.2Many home buyers in China are upper-middle-income and high-income households and they often own

multiple homes for investment purposes (see Section 2). Survey data also show that the majority (62% in2012) of home buyers purchase houses for investment purposes.

1

What economic forces are at work to generate (and sustain) the great housing boom in

China? Why would entrepreneurs divert their rapidly rising wealth toward housing instead of

productive capital? What are the economic and welfare consequences of such a paradoxical

housing boom?

In this paper, we propose a theory to explain the great housing boom. The key element

in our theory is a prolonged economic transition (after economic reform) featuring massive

resource (such as labor) reallocation from a conventional less productive sector to an emerg-

ing sector consisting of productive but financially constrained entrepreneurs. The rate of

return to capital in the emerging sector remains exceptionally high over the transition pe-

riod because of the large pool of “surplus” labor gradually unleashed from the traditional

sector. However, such high capital returns in the emerging sector– driven mainly by resource

reallocation– are not sustainable in the long run. Thus, a suffi ciently low rate of return to

capital in the remote future generates expectations of high future demand for alternative

stores of value (such as housing).

In a financially backward economy with capital controls and a limited supply of financial

assets, such rational expectations can lead to great current demand for housing by entre-

preneurs in the emerging sector, even if housing provides no rents or utilities– which means

that a housing bubble will arise in China after the housing market reform in the late 1990s.3

More importantly, the growth rate of a housing bubble will be dictated by the rate of return

to capital in the emerging sector. This implies that the bubble (if one emerges) is predicted

to grow much faster than aggregate income during the economic transition.

The key mechanism behind this theory of a faster-than-income growing housing bubble

hinges on the notion of “marginal investors” in the housing market: The rate of capital

returns facing productive entrepreneurs will dictate the bubble’s growth rate. In other

words, our theory implies that the participation of other agents facing lower capital returns

or interest rates– the non-marginal investors– can affect only the level of housing prices, not

the growth rate of housing prices. To support such a marginal investor theory, we present

empirical evidence at both the city and firm levels. Among other things, we document an

important empirical fact that the rate of private returns to capital across major Chinese

cities is highly predictive of the city’s excessive housing price growth above its disposable

3The implications of our model are not restricted to housing bubbles. Chinese investors have indeedspeculated on various “valueless” assets and storable goods as alternative stores of value, such as stamps,garlic (similar to tulip bulbs), tea, salt, and art, among others. They have also speculated in the stockmarket, which resulted in stock market bubbles. But these bubbles have burst from time to time due toeither the quite limited market size (such as garlic) relative to China’s astronomical stock of savings or thelack of critical regulations to mitigate risks (especially in the case of the stock market). Hence, the housingmarket has become the relatively more attractive and stable market for speculators, given its enormousmarket size and relatively higher transparency and lower volatility than the stock market.

2

income growth.

We show that with such a mechanism, a calibrated model can quantitatively replicate

China’s house price dynamics over the past decade fairly well and still be consistent with

many other salient features of the Chinese economy. Our theory also predicts that such

an abnormally fast-growing housing bubble will lose steam as the economy approaches the

Lewis turning point when the surplus labor is exhausted. This prediction is consistent with

the recent data from China.

Our paper fits into the fast-growing literature on economic development and resource

misallocation under financial frictions.4 In such an environment, following policy reforms

that remove important sources of resource misallocations, there exists a prolonged transition

in which capital and labor are reallocated gradually from the less productive sector to the

more productive (but financially constrained) new firms. While the bulk of the literature

emphasizes the effects of resource reallocation on improving allocative effi ciency and the

associated saving-investment dynamics during the transition, we argue that such a transition

may also be prone to asset bubbles, especially growing bubbles, even when the economy enjoys

fast productivity growth and high returns to capital. This prediction is also supported by

evidence from other emerging economies in Asia, such as Korea, Taiwan, and Vietnam, which

experienced faster-than-income growth of housing prices during their respective economic

transition periods featuring labor reallocation from traditional less productive sectors to the

emerging and more productive sectors.

To incorporate asset bubbles into such a transition economy, we extend the framework

of Song, Storesletten, and Zilibotti (SSZ, 2011) to a setting with an intrinsically valueless

asset– housing. The SSZ model is attractive for our purposes because it can endogenously

generate and quantitatively account for some important features of China’s economic tran-

sition, such as a persistently high rate of aggregate income growth and persistently high

returns to capital in the emerging sector, which we argue are key to understanding China’s

prolonged paradoxical housing boom. A nice property of the SSZ model is that it features

an endogenous AK growth period during the economic transition, which can sustain a con-

stant and exceptionally high rate of return to capital in the private sector for a prolonged

period without diminishing returns, consistent with Chinese data on capital returns. Once

the transition ends, however, the model reaches a Lewis turning point without surplus labor

and starts to behave like a standard neoclassical model with declining returns to capital and

GDP growth rate. Our contribution and value added is to show that such a development

4See, for example, Jeong and Townsend (2007); Restuccia and Rogerson (2008); Guner, Ventura, and Xu(2008); Song, Storesletten, and Zilibotti (2011, 2014); Buera, Kaboski, and Shin (2011); Buera and Shin(2013), Moll (2014) and Midrigan and Xu (2014).

3

path can sustain growing bubbles– bubbles that grow much faster than aggregate income

despite an exceptionally high rate of return to capital.

Our paper is one of the first to study growing bubbles, as opposed to static bubbles or

bubbles that grow at or below the growth rate of the economy.5 In addition, our model

sheds light on the economic and welfare implications of China’s housing bubble: It can

significantly prolong China’s economic transition and reduce social welfare. Unlike many

traditional bubble models where bubbles are welfare improving because of the existence of

dynamic ineffi ciency, in our model bubbles can exist even when the economy is dynamically

effi cient, thanks to the disparity between social and private rates of return to capital. That

is, our model economy is dynamically effi cient from a social perspective even though it

is dynamically ineffi cient from the private sector’s view point.6 Hence, by crowding out

private capital formation and other productive activities, the growing bubble in our model

creates a severe negative externality on the permanent income of all agents.7 Accordingly, the

occurrence of the housing bubble generates a substantial degree of resource misallocation and

welfare losses, prolonging economic transition and slowing aggregate economic growth. Such

adverse welfare consequences offer an appealing explanation and rationale for the Chinese

government’s concerns over the great housing boom and its policies to contain the bubble.

Our paper also contributes to the emerging literature on China’s high housing price

puzzle. Most theoretical works in this area focus on why the housing price level is so high in

China. For example, Wei, Zhang, and Liu (2012) provide a theory to link the high housing

price levels in major cities in China to high household saving rates in these areas due to

an unbalanced gender ratio.8 In sharp contrast, our paper focuses on why housing prices

in China have been able to grow much faster than the economy over a prolonged period.

Models that explain only the high housing price level from the demand side are insuffi cient to

understand China’s growing housing bubble, which suggests that China’s housing price level

is too low instead of too high relative to its long-run equilibrium level. Hence, by shifting the

5For the rapidly developing housing bubble literature, see Caballero and Krishnamurthy (2006); Kocher-lakota (2009); Farhi and Tirole (2012); Giglio and Severo (2012); Martin and Ventura (2012); Ventura (2012);Burnside, Eichenbaum, and Rebelo (2013); Miao and Wang (2013); and Galí (2014), among many others.

6See also Farhi and Tirole (2012) for a similar result. In both papers, agency frictions drive a wedgebetween the social rate of returns to capital and the equilibrium rate of returns. Accordingly, bubbles existeven in an environment with dynamic effi ciency. However, the reason bubbles may reduce welfare differsbetween our paper and theirs. In their paper, the presence of bubbles raises the equilibrium interest rate,which reduces the price of other external liquid assets.

7See the next section for empirical evidences on the housing bubble’s crowding-out effect on China fixedcapital formation.

8Wang and Wen (2012) argue that high housing prices cannot explain China’s high average householdsaving rate. Instead, the culprit lies in China’s rapid income growth in conjunction with precautionarysaving under borrowing constraints due to market incompleteness and idiosyncratic consumption/incomerisks (Wen, 2009).

4

analysis from the level of housing prices to the growth rate of housing prices, our paper sheds

light on China’s housing price dynamics, as well as why such a growing housing bubble may

create resource misallocation and prolong China’s economic transition, an issue unaddressed

in Wei, Zhang, and Liu (2012).

The remainder of the paper is organized as follows: Section 2 presents some institutional

backgrounds and stylized facts about China’s housing market to frame the questions we

raise and support the key assumptions in our theoretical model. Section 3 describes a simple

two-period benchmark model to illustrate our essential explanations of the great housing

boom, as well as the model’s qualitative implications. Section 4 extends the analysis to

a multiperiod version of our model for a quantitative analysis. Section 5 concludes with

remarks for further research.

2 Stylized Facts

2.1 Housing Price Growth and Vacancy Rate

It is well known that the offi cial housing price indices published by the Chinese government

suffer from many measurement problems and do not control for housing quality. Hence, they

tend to severely underestimate the growing trend of China’s housing prices.9 To correct such

problems, Wu, Deng, and Liu (2014) use independently constructed housing price indices

based on sales of newly built housing units in 35 major Chinese cities. These city-level series

are then aggregated into a national level indicator using a weighted average formula, with

the total transaction volume during 2006-2010 in each city as the weight. The resulting

national-level housing price index shows a much faster growth rate than the offi cial housing

price index. For example, the national-level real housing price index has increased at a rate

of 17% per year between 2006:Q1 and 2010:Q4. If we ignore the negative impact of the 2008

financial crisis, the average growth rate of housing prices was about 20% per year during

this period (see Figure 1, solid line with circles).

The increase in housing prices is also accompanied by rapidly rising land values in China.

Figure 1 (dashed line with stars) shows that nationwide real constant quality land values

have grown at an average rate of more than 16% per year between 2004:Q1 and 2013:Q2.

Accordingly, land value has constituted an important and increasing share in housing prices.

9For example, the National Bureau of Statistics of China (NBSC) provides two major housing priceindices. Based on these housing price indices, the average growth rate of housing prices in China is belowthe average growth rate of the economy. However, Wu, Deng, and Liu (2014) argue that these measures areseverely biased downward because they fail to control both the complex-level quality changes (e.g., housingsuburbanization) and unit-level quality changes (e.g., developers’pricing strategies).

5

For example, according to Wu, Gyourko, and Deng (2012), in the city of Beijing the average

share of land value in housing prices was 37% before 2008 and surpassed 60% after 2010.

The faster-than-income growth rate of housing prices is prevalent across almost all major

cities in China. Figure 2 shows that most of the 35 major cities in China have experienced a

significantly faster growth rate in housing prices than city-level aggregate disposable income,

which takes into account population growth due to migration. For example, in large cities

such as Shanghai and Beijing, the average real growth rate of housing prices during the

same period is 2 to 3 times higher than the respective real growth rate of disposable income.

The fact that house prices grow persistently faster than aggregate disposable income at

both the national and the city levels casts doubt on the conventional wisdom that China’s

housing price growth is driven mainly by the increased utilitarian demand for housing due

to rural-to-urban migration, or solely by the rapidly increasing purchasing power of Chinese

citizens.10

In another important empirical study, Fang, Gu, Xiong and Zhou (2015) use an inde-

pendent data source based on 120 Chinese cities to document the patterns of housing price

growth and per capita aggregate income growth in the sample period of 2003-2013. Among

other things, they found that housing prices grew persistently faster than per capita dis-

posable income or gross regional product in the first- and second-tier cities in China. Such

evidence is consistent with that presented by Wu, Deng and Liu (2014).

Along with the great housing boom is the continuously rising and alarmingly high housing

vacancy rate. According to the China Household Finance Survey (2014), in 2013 the average

vacancy rate in the first-, second-, and third-tier cities in China was 21.2%, 21.8%, and

23.2%, respectively.11 ,12 Among different groups of households, 35.1% of entrepreneurial

households own vacant houses (or 29.9% of them have multiple apartments). Furthermore,

the proportion of households with vacant houses increases with household income. In the

top 10th percentile income group, for example, 39.7% of households have vacant (multiple)

houses, which is about 22 percentage points higher than households in the lowest income

quantile.

The faster-than-income growth of housing prices implies a rapidly rising price-to-income

ratio for average wage earners. Ge and Yang (2014) use data from the China Household

10See Garriga et al. (2014) for the migration view of China’s housing price boom.11The definition of the vacancy rate in China corresponds to the homeowner vacancy rate in the Housing

Vacancy Survey conducted by the U.S. Census Bureau, computed as the proportion of the vacant self-ownedhousing units in total homeowner housing units. The definition of vacant housing units does not includehousing units that are newly built but not yet sold.12China’s first-tier cities usually refer to Beijing, Shanghai, Guangzhou, and Shenzhen, which constitute

“The Big 4.”Second-tier cities include the provincial capital cities and other municipalities directly underthe central government. Third-tier cities include all other cities.

6

Income Survey (2014) and find that the growth rate of real wages has been increasing since

the economic reform. Between 1998 and 2007, the average real wage growth reached 9.0%

per year, almost as fast as real per capita GDP growth.13 However, housing prices have

been growing much faster. The gap between real housing price growth and real wage growth

is more than 8 percentage points. With a rising housing price-to-income ratio, it becomes

increasingly diffi cult for the average Chinese household, especially low-income households

who do not yet own a house or want to purchase additional houses, to use housing as a store

of value. Nonetheless, data show that even those in the bottom income cohort of China’s

urban population have engaged in housing investment despite the excessively high price-

to-income ratio. The explanation could be simple: Suppose rational home buyers expect

housing prices to growth faster than their disposable income; they would opt to jump into

the housing market sooner rather than later if they want to become homeowners during their

lifetime. Hence, the fact that China’s rapidly rising housing prices have not discouraged and

prohibited households in the lowest income range to buy houses, despite severe borrowing

constraints and a more than 30% down payment requirement, suggests that they either

observe or expect housing prices to grow significantly faster than their incomes.

2.2 Returns to Capital and Resource Reallocation

It is well documented that the average real rate of return to capital in China has remained

around 20% over the past decade (see, e.g., Bai, Hsieh, and Qian, 2006). Following this

literature, we reconfirm this finding here, using the marginal revenue product of capital as

a proxy for the rate of return to capital (as in Bai, Hsieh, and Qian, 2006).14 ,15 Panel A

of Figure 3 shows that the real rate of return to capital was on average 20% between 1998

and 2012.16 In particular, it increased steadily from 18% in 2001 to 26% before the financial

crisis year of 2008. Similarly, the measured average after-tax real rate of return to capital

(excluding urban housing) was about 18.2% between 1998 and 2012, approximately the same

13According to the data from the NBSC, the national average growth rate of real per capita disposableincome between 1998 and 2012 was 9.3% per year.14Specifically, we measure the capital-to-output ratio at market prices and include any expected change in

the price of capital as part of its returns. Our computed series of the marginal (revenue) product of capitalbetween 1998 and 2005 are essentially the same as those of Bai, Hsieh, and Qian. (2006).15Ideally, we should use the income share of reproducible capital. In China, however, the data on repro-

ducible capital income are not available, since there was no market for land in China before the mid-1990sand the market for leaseholds is very imperfect. Bai, Hsieh, and Qian (2006) find that after 1990 the mea-sured average rate of return to capital is close to its counterparts in the non-agricultural and non-miningsectors.16Until 2005, the Chinese statistical authorities classified all self-employment income as labor income.

Therefore, if anything, the reported capital share understated the true capital income at least before 2005.

7

as the estimated growth rate of the aggregate housing prices in real terms.17

Underlying the enduring high rate of return to capital is the massive labor reallocation

in China. Panel B of Figure 3 plots the evolution of the share of private employment in total

employment. Following SSZ, we adopt two measures of the private employment share: (i) the

share of domestic private enterprises (DPEs) in total employment (which equals employment

in DPEs plus SOEs); and (ii) (DPE+FE)/(DPE+FE+SOE+COE), where FE pertains to

employment of foreign enterprises, COE that of collectively owned enterprises, and SOE

that of state-owned enterprises. For both measures, the private employment share increased

steadily for most years during the 1998-2011 period and surpassed 60% in 2011. We believe

the massive degree of labor reallocation from SOEs to the emerging private firms and the

associated low wage rate are key to sustaining the prolonged high rate of return to capital

in China over the past decade despite a high investment rate.

2.3 Empirical Evidence Consistent with the “Marginal Investor”

Hypothesis

A crucial premise in our theoretical model to simultaneously explain the three stylized facts

of China’s great housing boom is the marginal investor hypothesis– that the faster-than-

income growth rate of housing prices (despite high capital returns and a high vacancy rate)

is driven mainly by speculative housing demand from agents (entrepreneurs) in the produc-

tive sector of the economy who have access to high capital returns. Hence, the higher the

private rate of return to capital, the higher the rate of housing price growth above the ag-

gregate income growth. Standard economic theories would find it puzzling and paradoxical

that well-to-do entrepreneurs and productive firms with high capital returns would engage in

speculative housing (or real estate) investment. Such theories would find it even more puz-

zling that private firms’capital returns across different cities are positively correlated with

or predictive of these cities’housing price growth in excess of their aggregate income growth.

In what follows, we document precisely such stylized facts from three different perspectives.

First, we use household-level evidence to show the predictive power of the entrepreneurial

status in the vacancy rate of a city’s housing market. Second, we conduct cross-city panel

regression analysis to show a strong empirical linkage between excess housing price growth

above disposable income growth and the rate of return to capital facing private firms across

17The measured after-tax returns to capital excluding urban housing are computed by excluding the urbanresidential capital stock from the measured capital stock and by excluding its imputed rent (assumed as 3%of the original value of the residential capital stock by the NBSC) and tax on output and enterprise incomefrom the capital income.

8

different regions. Finally, we use firm-level data to reveal the extent of firm involvement in

real estate investment and the linkage between their capital returns and ownership structure.

2.3.1 Household Evidence

As noted earlier, China’s average vacancy rate is at least as high as 22.4% across cities in

2011– nearly a quarter of privately owned housing units in China are unoccupied (by owners).

What explains such a high homeowner vacancy rate? The China Household Finance Survey

(2014), which conducts regression of housing vacancy status against an exhaustive list of

both household-level and macro-level variables, shows that the homeowner’s entrepreneurial

status (i.e., whether the homeowner owns a private business) has a strong predictive power

on the vacancy status of the housing units in all Chinese cities. In other words, entrepreneurs

with access to alternative asset (capital) returns are more likely to own multiple unoccupied

housing units than other homeowners. This fact holds true even if the regressions control for

household incomes, the education level of the household head, attitude for risky investment,

housing price-to-rent ratio, urbanization rate, and whether the family has male members to

be married (see Table 1 of the CHFS, 2014). Notice that entrepreneurs account for 17% of

China’s urban population and that, conditional on holding vacant housing units, 25% of the

homeowners are entrepreneurs.

2.3.2 Cross-City Evidence

The concept of the marginal investor in our model is borrowed from the asset pricing litera-

ture, where the excessively high rate of return to risky assets is determined by the marginal

investor who is able to participate in such assets market without being borrowing con-

strained. In our model, the marginal investors in the housing market are the entrepreneurs

who have access to the high capital returns and yet decide to also participate in the housing

market. Such alternative asset returns to the marginal investors will dictate the rate of re-

turn to housing investment in a self-fulfilling housing bubble equilibrium by the no-arbitrage

condition.

As far as we know, the best empirical approach to support the marginal investor theory

in the asset pricing literature is to assess the predictive power of the investors’marginal

value of wealth (proxied by their leverage position) on the excess asset returns (see, for

example, Adrian, Etula, and Muir, 2014). Here we follow a similar strategy by investigating

the predictive power of private capital returns in different cities on the excess housing price

growth (i.e., the growth rate of housing prices minus the growth rate of aggregate disposable

9

income). Our evidence suggests that (i) across major Chinese cities the private rate of

returns to capital is a strong predictor of the city’s excess housing price growth and (ii)

capital returns of private firms have a larger and more significant predictive power on excess

housing returns than do capital returns of SOEs.

Specifically, we measure capital returns in a region as the ratio of total profit to the net

value of fixed assets. We run the panel fixed-effect regression of excess housing price growth

against the capital returns of different types of firms in different regions. Our panel data

cover excess housing price growth and capital returns for 35 majors cities in China between

2006 and 2010. Table 1 reports the results from our panel regression with excess housing

price growth as the dependent variable. Columns (1) and (2) suggest that capital returns are

highly significant in predicting excess housing returns regardless of the firm type. Column

(3) shows that when both types of firms are included as independent variables, the capital

returns of POEs exhibit a more significant and stronger predictive power on excess housing

price growth than those of SOEs. This evidence suggests that private enterprises are more

likely to be the marginal investors in the housing market than are SOEs.

Quantitatively, Column (3) of Table 1 implies that a 1-percentage-point higher rate of

capital return for private firms in a city at a particular time point would predict a 0.7-

percentage-point higher housing price growth above income growth in that city. For example,

Beijing’s private real rate of return to capital between 2006 and 2010 is 29.23% and its excess

housing price growth rate is 18.78 percentage points in the same period, whereas in Lanzhou

(the capital of a northwestern province) the aggregate capital returns was 9.76% per year in

the same period. So there is a 19.47-percentage-point gap for capital returns between these

two locations, which would predict Lanzhou’s excess housing price growth to be about 5.15

percentage points. In the data, Lanzhou’s excess housing price growth was 5.06 percentage

points above its aggregate income growth, which is consistent with the prediction of our

regressed results.18

2.3.3 Firm Evidence

Firm-level data show that a substantial fraction of non-real estate firms (including the very

productive ones) in China engage in real estate investment that is unrelated to their original

business. This stylized fact indicates not only a close link between capital returns and

18Although correlation is not causation, the reverse of the causal linkage (that high housing price growthcauses a high profit ratio or rate of return to capital) is a less appealing theory because it fails to explainwhy housing price growth is excessively high in the first place and why it would necessarily lead to highcapital returns.

10

housing returns, but also a possible source of the crowding-out effect of the housing bubble

on capital investment, as we show in the next section.

Here we use the data on publicly listed firms, based on the China Stock Market &

Accounting Research (CSMAR) database, to check the extent of involvement by non-real

estate firms in real estate investment and issues related to our marginal investor hypothesis.

We restrict our sample to firms that have been traded for at least two years on the China

A-share stock market over the period of 2007- 2013.19 We exclude firms in the real estate

and construction sectors.

Table 2 reports the summary statistics of non-real estate firms with investment in real

estate that is unrelated to their original business. About 45 percent of firms have such

investment properties (purchased for rent and capital gain, instead of as a necessary input

or production factor in their own business).20 The share of real estate investment property

in the total physical assets of these firm is 15% on average and is stable over time.

We now examine the capital returns of these firms investing in the housing market. We

argue that if both private and SOE firms invest in the housing market, firms with higher

capital returns tend to be the marginal investors. Our evidence shows that among those

non-real estate firms involved in real estate investment, SOEs on average have lower capital

returns (productivity) than POEs.

Specifically, using the above sample of firms, we regress capital returns against the degree

of state ownership. We construct capital returns at the firm level using the ratio of operating

profit to the one-period lag of property, plant, and equipment (PPE), which have been

excluded from the value of investment property since 2007. We adopt three different measures

to gauge the degree of state ownership. The first is a direct measure of the state-owned stock

share; the second and third measures pertain simply to state-ownership dummies. For the

second measure, we let the state-ownership dummy have a value of 1 if its state-owned stock

share exceeds 50%. For the third, we let the dummy have a value of 1 if the state-owned

stock share exceeds 25%. To be consistent with our model’s assumption, we also add an

one-digit industry dummy.21 Table 3 reports the estimated coeffi cients on the measured

19Since January 1, 2007, all Chinese listed firms have been required to disclose their real estate holdingsfor investment purposes, which includes any land and buildings held for rental income and/or for capitalappreciation purposes.20As mentioned by Li, Shao, and Tao (2015), prominent examples of non-real estate firms diversifying into

real estate include Youngor (a leading garment company), Kweichow Moutai (a leading liquor company),and Suning (a leading electronics retailer).21The empirical model is

KPit = cons+ β × Sit +∑j∈J

γj × Ind_dumji + εit

11

state ownership. Clearly, for all three measures, the return to capital is indeed negatively

correlated with the degree of state ownership among the firms investing in real estate.22

This, again, suggests that private enterprises tend to be the marginal investors in the housing

market.

To sum up, the empirical evidence presented in this section supports our marginal in-

vestor hypothesis in that (i) entrepreneurs or productive firms are extensively involved in the

housing market and are an important determinant of China’s high vacancy rate; (ii) private

capital returns are highly predictive of the excess housing price growth above income growth

across major cities in China; and (iii) on average, the capital returns of SOEs (that invest in

the housing market) are lower than those of POEs and are less predictive of excess housing

price growth across major cities.

2.4 Crowding-Out Effects on Capital Investment

The rapid growth in housing prices is accompanied by a spectacular boom in the real estate

sector. Data from the China Statistical Yearbook (CSY) 2012 show that the share of total

real estate investment in GDP increased by more than threefold, from 4.2% in 1999 to 13.2%

in 2011. Booming residential investment accounts for about 70% of the real estate boom.

The average nominal growth rate of residential investment is 25.5% per year, compared with

an average nominal GDP growth rate of 13.9% per year. Accordingly, the share of residential

investment in GDP rose from 2.4% in 1999 to 9.5% in 2011, a fourfold expansion.

On the other hand, the rapidly growing housing bubble has shown a strong crowding-out

effect on China’s capital formation for both SOEs and POEs. We measure the crowding-out

effects by estimating the correlation coeffi cients between housing price growth and non-real

estate investment growth.23 To remove seasonal effects, all growth rates are on a year-to-

year basis, which means the growth rate of a particular month is compared with the same

month in the previous year. Table 4 presents the correlation between real housing price

growth (deflated by the consumer price index) and real investment growth (deflated by the

producer price index). The second and third columns show the correlations of aggregate

housing price growth with growth in real estate investment and other types of investment,

where KP denotes the capital returns, Sit is the measure of the degree of a firm’s state ownership, andInd_dum is the industry dummy.22This does not rule out the possibility that in some industries monopolized by SOEs (e.g. petroleum),

SOE firms investing in the property market can also enjoy very high revenue-based productivity.23Due to data availability constraints, we are able to decompose aggregate investment into only real estate

investment and the rest.

12

respectively. In addition to reporting the contemporaneous correlations, we also report lead

and lag correlations.

Table 4 shows that the growth of real estate investment is significantly and positively

correlated with housing price growth, while non-real estate investment is significantly nega-

tively correlated with housing price growth. More importantly, the results show that current

growth in housing prices is a strong predictor of a future drop in non-real estate investment

growth, with the peak correlation between housing price growth and investment growth

reached at a 5-month lead. This crowding-out effect of housing price growth on non-housing

investment is consistent with the predictions of our model.24

Our findings of crowding-out effects of housing investment are also supported by indepen-

dent empirical studies. For example, Li, Shao, and Tao (2015) find that firms with real-estate

investment property tend to experience under-investment in fixed capital formation by 10%

compared with their industry benchmark. Wu, Gyourko, and Deng (2015) find that, for

publicly listed firms, real estate value has no impact on fixed capital investment via the

collateral channel, further suggesting that real estate investment crowds out fixed capital

formation. Similarly, Chen, Liu, and Zhou (2013) provide empirical evidences that increases

in real estate prices tend to crowed out firms’fixed capital formation in China.

2.5 Other Facts Concerning Model Assumptions

Our model makes the following simplifying assumptions: Both the land supply and the

interest rate are fixed. In addition, our model focuses on housing price dynamics over the

past decade, which corresponds to a period of massive SOE privatization in China.

SOE Reform. Under China’s planned economy, SOEs were the major employers in cities

and played the pivotal role of maintaining low unemployment and ensuring social stability.

By the mid-1990s, the Chinese government realized that its gradualist reform policy could

no longer manage the mounting losses of SOEs. Beginning in 1997, China moved forward

with more aggressive restructuring with large SOEs, accomplished through large-scale pri-

vatization. The reallocation of labor and capital from SOEs to POEs has been a key source

of productivity growth in the past decade.

Land Supply. In China the land available for home construction is strictly controlled by

the government. During 1997-2000, land available for new construction was limited to 20.40

million acres; during 2001-2010, it was limited to no more than 30.72 million acres. This

restriction on the size and new release of construction land was further strengthened by the

24A wide class of models (e.g., Kocherlakota, 2009 and Martin and Ventura, 2012) predicts that housingbubbles, by serving as collateral, crowd in capital investment.

13

National Land Use Plan 2006-2020, passed by the State Council of China in August 2008.

According to this regulation, the total land available for construction in urban and rural

areas is limited to 506.25 million acres by 2010 and 558.6 million acres by 2020. The same

plan requested that the amount of cultivated land in 2010 and 2020 be maintained at 1.818

billion acres and 1.805 billion acres, the so-called red line lower limit for the total amount of

arable land. Figure 4 shows the total amount of arable land in China. It is clear that since

2003 the amount of arable land has been more or less stabilized, implying a de facto fixed

supply of land for home and real estate construction.25

Financial Repression and Interest Rate Control. China has made significant progress

since 1978 in opening its economy to the outside world, but financial reform significantly

lags its economic reform in goods-producing sectors. China’s financial repression is easily seen

in Figure 5 where interest rates are essentially flat with the deposit rate substantially below

the lending rate. Funds are channeled through state-owned banks to the conventional sector

occupied mainly by SOEs. There are few investment alternatives for household savings:

Stock markets are poorly regulated and dominated by SOEs, interest rates are set by the

government, the national capital account is closed, and the exchange rate is fixed or tightly

managed. Through a system of strict capital controls where the state directly manages the

banking sector and financial intermediation, the government has been able to maintain or

suppress interest rates at below market-clearing levels. When the interest rate is fixed at

a level below the market-determined rate, SOEs are able to survive despite productivity

ineffi ciency.

3 The Benchmark Model

In this section, we develop a theory of China’s great housing boom consistent with the

institutional background and stylized empirical facts about China and its housing market

behaviors. In particular, we extend the SSZ model to a setting with an intrinsically valueless

asset– housing– and prove that a housing price bubble that grows faster than GDP exists

even if housing provides no rents or utilities to investors. For simplicity we exclude the access

of low-income households (workers) to the housing market because their participation has

only a level effect on the housing prices but no growth effects. We emphasize the growing

nature of the bubble because the traditional bubble literature often focuses exclusively on

static bubbles or bubbles that grow at most at the same rate as the economy, which is

contradicted by the Chinese data. In this section we illustrate our main story in a two-

25A relatively inelastic supply of land is crucial for the existence of a sustained housing bubble.

14

period overlapping-generations (OLG) model. We extend the model to a more realistic

setting with multiperiod OLGs for the quantitative analysis in Section 4.

3.1 The Environment

The economy is populated by two-period-lived agents with overlapping generations. Agents

work when young and consume the returns to their savings when old. Agents have heteroge-

neous skills. In each cohort, half of the population are workers without entrepreneurial skills

and the other half are entrepreneurs. Entrepreneurial skills are inherited from parents; we

do not allow transition of social classes (for simplification without loss of generality). The

total population Nt grows at an exogenous rate ν.

Before the economy starts, the government owns H units of housing (land), which are in

fixed supply. At the beginning of the first period, the government sells the housing stock to

the market (if there is demand) and consumes all the proceeds.

3.1.1 Technology

There are two production sectors and thus two types of firms. Labor is perfectly mobile

across the two sectors, but capital is not. The first sector is composed of conventional

firms– F-firms, which (for simplicity) are owned by a representative financial intermediary

(e.g., a state-owned bank) and operated as standard neoclassical firms.26

The second sector is a newly emerging private sector composed of unconventional firms–

E-firms. The E-firms are operated by entrepreneurs. More specifically, E-firms are owned

by old (parent) entrepreneurs, who are residual claimants on profits, and they hire their own

children as managers. Workers can choose to work for either type of firm.

E-firms are more productive than F-firms but are severely borrowing constrained– they

cannot borrow from each other or from any other sources. As a result, they must self-finance

capital investment through their own savings. In contrast, F-firms can rent capital from

their representative financial intermediary at a fixed interest rate R. Accordingly, F-firms

can still survive in the short run despite inferior technology. Over time, however, labor will

be gradually reallocated from F-firms to E-firms as the capital stock of E-firms expands.

Thus, the economy features a transition stage during which F-firms and E-firms coexist but

with the F-sector shrinking and the E-sector expanding. When the transition ends, only E-

firms exist and the economy becomes a representative-agent growth model with neoclassical

26We can assume that the F-firms have market power and our main results do not change qualitatively.

15

features. Our focus in this paper is on the transition stage.27

The technologies of the two types of firms follow constant returns to scale

yFt =(kFt)α (

AtnFt

)1−α, yEt =

(kEt)α (

AtχnEt

)1−α, (1)

where yj, kj, and nj denote per capita output, capital stock, and labor, respectively, for

a type-j firm, j ∈ {E,F}. The parameter χ > 1 captures the assumption that E-firms

are more productive than F-firms. Technological growth in both sectors is constant and

exogenously given by At+1 = At (1 + z). However, during the economic transition, resource

reallocation can generate endogenous growth faster than the growth in At.

3.1.2 Worker’s Problem

Workers can deposit their savings into the representative bank and earn a fixed interest

rate R. Without loss of generality, we assume that workers do not speculate in the housing

market. Allowing workers to invest in housing does not change our main results– although

the housing price level would be much higher, the growth rate of housing prices is unaffected.

This is because the equilibrium growth rate of housing prices in our model is determined

by the rate of return to capital of the entrepreneurs, who are the marginal investors in the

bubbly equilibrium.28

The worker’s consumption-saving problem is

maxcw1t,c

w2t+1

log cw1t + β log cw2t+1 (2)

subject to cw1t + swt = wt and cw2t+1 = swt R, where wt is the market wage rate, and cw1t, c

w2t+1,

and swt denote, respectively, consumption when young and consumption when old, and the

worker’s savings.

3.1.3 The F-Firm’s Problem

In each period, an F-firm maximizes profits by solving the following problem:

27Note that the concept of “transition” in this paper is different from the convention in the neoclassicalgrowth model, where transition means the dynamic path from an initial point toward the steady state. Thisconventional transition phase shows up in our model after the F-sector disappears. To avoid confusion, wecall this neoclassical transition period “post-transition.”28The proof is available upon request.

16

maxkFt ,n

Ft

(kFt)α (

AtnFt

)1−α − wtnFt −RkFt , (3)

where the rental rate for capital is the same as the deposit rate R. The first-order conditions

imply

wt = (1− α)At

(αR

) α1−α

. (4)

Note that during the transition, the wage rate, scaled by the level of technology, wt/At, is

constant, due to a constant rental rate for capital and, accordingly, a constant capital-to-labor

ratio, kFt /(Atn

Ft

)= (α/R)

11−α . When the transition is completed, all F-firms disappear, so

equation (4) no longer holds.

3.1.4 The E-Firm’s Problem

Following SSZ (2011), we assume that young entrepreneurs receive a management feemt from

their parents, which is a fixed ψ < 1 fraction of the output produced,mt = ψ(kEt)α (

AtχnEt

)1−α.29

Therefore, the old entrepreneur’s problem can be written as

maxnEt

(1− ψ)(kEt)α (

AtχnEt

)1−α − wtnEt (5)

The first-order conditions imply a linear relationship between nEt and kEt

nEt = [(1− ψ)χ]1α

(R

α

) 11−α kEt

χAt. (6)

Such a linear relationship is obtained because of a constant wage rate, which in turn results

from the constant interest rate R. Accordingly, labor is reallocated to E-firms at a speed

equal to the growth of the E-firm’s capital stock. Substituting (6) into (5) gives the E-firm’s

profit: π(kEt)

= (1− ψ)1α χ

1−αα RkEt ≡ ρEkEt , where the first equality is based on equation

29SSZ also provide a micro-foundation for a young entrepreneur’s management fee as a fixed fraction ofoutput: There exists an agency problem between the manager and owner of the business. The manager candivert a positive share of the firm’s output for her own use. Such opportunistic behavior can be deterredonly by paying managers a compensation that is at least as large as the funds they could steal, which is ashare ψ of output. An alternative interpretation of ψ is that it reflects the government policy that transfersresources from the capital owners (the old entrepreneurs) to the managers (the young entrepreneurs). SeeMiao, Wang and Zhou (2014), who study housing bubbles based on firm-level policy distortions.

17

(6). Whenever F-firms exist, the return to capital for E-firms, ρE ≡ (1− ψ)1α χ

1−αα R, is

a constant because nEt increases linearly in kEt . Similar to SSZ, we impose the following

assumption about an E-firm’s relative productivity such that an entrepreneur’s return to

capital is higher than the deposit rate R: χ > χ ≡(

11−ψ

) 11−α

.

3.1.5 The Young Entrepreneur’s Problem

The young entrepreneur decides consumption and portfolio allocations in housing invest-

ment, bank deposits, and physical capital investment. The rate of return to capital invest-

ment is simply ρE. We assume that the balanced growth rate, which equals the rate of

return to housing investment at steady state, is higher than the bank deposit rate– that is,

(1 + z) (1 + ν) > R. As a result, the entrepreneur will always prefer investing in housing

to depositing funds in the bank.30 Given the housing prices, denoted as PHt , the young

entrepreneur faces a two-stage problem.

In the first stage, a young entrepreneur’s consumption-saving problem is

maxsEt

log(mt − sEt

)+ β logRE

t+1sEt , (7)

where REt+1 ≡ max

{ρE, PH

t+1/PHt

}is the rate of returns for entrepreneurial savings and de-

pends on the entrepreneur’s portfolio choice. First-order conditions give the optimal savings

of young entrepreneurs, sEt = mt/(1 + β−1

).

In the second stage, the young entrepreneur chooses portfolio allocation given the total

savings sEt . The fraction φEt of savings is invested in capital such that K

Et+1 = φEt s

Et Nt,

where KEt+1 = kEt+1Nt+1 is the total capital deployed by E-firms. The remaining (1 − φEt )

fraction of savings is invested in housing, such that PHt H

Et =

(1− φEt

)sEt Nt, where HE

t

denotes the total housing stock purchased by young entrepreneurs in period t. Throughout

this paper, we ensure there exists an interior solution for portfolio choice, such that the

following no-arbitrage condition holds:

PHt+1

PHt

= ρEt+1, (8)

30We will show that the housing price growth rate is constant in the transition stage and declines towardthe steady-state level after the transition.

18

where ρEt+1 = ρE (a constant) during the transition. Hence, an old entrepreneur’s income is

simply ρEsEt . The above condition simply says that the rate of return to housing must equal

the rate of return to entrepreneurial capital in a bubbly equilibrium.

3.1.6 The Bank’s Problem

For easy of exposition, we assume that each period the bank simply absorbs deposits from

young workers, rents them to F-firms at interest rate R, and invests the rest in foreign bonds

with the same rate of return R (as in SSZ, 2011). As mentioned earlier, the result would

be similar if we instead allowed the bank to also invest in housing on behalf of the workers

and the F-firms. This is so because the F-firm is not the marginal investor determining the

growth rate of housing prices in the housing market.

3.1.7 Time Line

To summarize, in each period the economic events unfold as follows:

1. At the beginning of period t, production of E-firms and F-firms takes place. Each

young worker gets paid a real wage wt regardless of which sector they work in. Each

young entrepreneur gets mt.

2. Both the young entrepreneur and young workers make consumption and saving deci-

sions. In addition, the young entrepreneur makes a portfolio choice φEt .

3. The housing market opens. Old entrepreneurs sell housing stock held in the previous

period, HEt−1. Young entrepreneurs make a portfolio decision φ

Et .

4. F-firms repay their capital rents to the bank.

5. The currently old workers consume and die, as do the currently old entrepreneurs.

3.1.8 Law of Motion

Since E-firm is self-financed, the law of motion for the E-firms’capital stock follows

KEt+1 = φEt

ρEt ψ

(1− ψ)α

1

1 + β−1KEt , (9)

where ρEt = ρE for all periods during the transition. As shown later, in this simple economy,

the entrepreneur’s portfolio share in physical capital, φEt , is a constant, which, together

19

with a constant ρE, implies that the dynamics of the model have an AK feature during

the transition: The growth rate of E-firms’capital is constant. Similarly, we can obtain the

implicit law of motion for housing demand as

PHt H =

(1− φEt

) ρEt ψ

(1− ψ)α

1

1 + β−1KEt , (10)

where we have used the housing market-clearing condition HEt = H.

3.1.9 Post-Transition Equilibrium

We now characterize the equilibrium in the post-transition stage. Since nEt = 1, the profit

of the E-firm is

π(kEt)

= α (1− ψ)(kEt)α

(Atχ)1−α . (11)

Note that π(kEt)features decreasing returns to scale at this stage. The rate of return to

E-firms’capital is simply ρEt+1 = α (1− ψ)(kEt+1

)α−1(At+1χ)1−α .

3.1.10 The Steady State

The steady state of the economy is reached only in the post-transition stage. Since all per

capita variables (except labor inputs and housing) grow at the rate At, we detrend them as

xt = xt/At.

At the steady state, the law of motion for capital (9) implies

kE∗ =

[ψφE∗χ1−α(

1 + β−1)

(1 + z) (1 + ν)

] 11−α

. (12)

Since ρE∗ = α (1− ψ)(kE∗/χ

)α−1, we have

ρE∗ = α (1− ψ)

(1 + β−1

)(1 + z) (1 + ν)

ψφE∗. (13)

Equation (13) implies that the rate of return to capital is negatively related to the E-firms’

portfolio share in physical capital, φE∗.

20

The equilibrium portfolio allocation φE∗ can be solved by the no-arbitrage condition.

Since the supply of housing is fixed, the growth rate of housing prices, denoted as ρHt+1 ≡

PHt+1/P

Ht , equals the balanced growth rate, (1 + z) (1 + ν), in the steady state. As a result,

the no-arbitrage condition implies the E-firms’steady-state portfolio share in physical capital

is

φE∗ = α (1− ψ)(1 + β−1

)/ψ. (14)

Intuitively, the larger the rate of returns to E-firms’ capital, as captured by α (1− ψ) ,

the larger the share of entrepreneurial savings in physical capital. On the other hand, the

larger ψ and β, which imply, respectively, a larger income share and saving propensity of

young entrepreneurs, the lower the return to physical capital and thus the lower the share

of entrepreneurial savings in physical capital.

Note that, in our model, due to the presence of agency frictions (i.e., ψ > 0), there is a

wedge between the private and the social rates of return to capital. The social rate of return

to E-firms’capital is simply the marginal product of E-firms’capital, denoted as MPKE.31

By the definition of ρE, we then have ρE < MPKE. Hence, in contrast to the standard

bubble theory, dynamic ineffi ciency is a suffi cient, but not necessary, condition for housing

bubbles to exist in the long run. This has dramatically different and important welfare

implications from those of the traditional bubble literature, as we show below.

3.2 Characterizing the Bubbly Equilibrium

In this subsection, we explore the equilibrium with housing bubbles. We first discuss the

necessary conditions for housing bubbles to exist. We then show under which condition the

equilibrium path with housing bubbles can be achieved. Next, we derive the growth rate

of housing prices relative to that of aggregate output. Finally, we explore the normative

implications of bubbles.

3.2.1 Existence of Bubbles

Note that there always exists an equilibrium without bubbles in our model– that is, all

financial resources are invested in capital and φEt = 1 for all t. We call this equilibrium

the “fundamental equilibrium.”To understand the conditions for the existence of a bubbly

equilibrium, we must understand the nature of the fundamental equilibrium to know under

31Implicitly, the planner solves a constrained optimization problem without agency frictions but withfinancial market imperfectness as in the benchmark model.

21

which conditions in the fundamental equilibrium a bubbly equilibrium can emerge.

Consider the steady state first. The necessary condition for a housing bubble to exist in

the steady state (i.e., φE∗ < 1) is that in the fundamental equilibrium the rate of returns

to E-firms’ capital is below the balanced growth rate. In other words, the economy is

dynamically “ineffi cient” from the perspective of the entrepreneurs. Intuitively, when the

returns to capital are so low in the fundamental equilibrium, it is optimal for entrepreneurs

to divert savings into housing as an alternative store of value. This condition, together with

(14) , implies the following parameter restriction on the bubbly equilibrium:

α (1− ψ)(1 + β−1

)< ψ, (15)

or ψ > ψ ≡ α(1 + β−1

)/[1 + α

(1 + β−1

)]. Intuitively, a larger ψ makes the bubble more

likely to occur in two ways: First, it directly reduces the entrepreneur’s rate of return to E-

firms’capital. Second, by increasing the output share of the young entrepreneur, it increases

the capital stock accumulated by the young, thus lowering the marginal product of E-firms’

capital.32

We are now able to characterize the conditions for the existence of bubbles in both the

transition and the post-transition stages. Assumption (15) , together with the law of motion

for capital, (9), implies that in the fundamental equilibrium, we must have

KEt+1 > ρEt K

Et , ∀t. (16)

This is so because the wedge between KEt+1 and ρEt K

Et is a constant, and this constant

exceeds 1 in the fundamental equilibrium. Accordingly, given that (16) is satisfied at the

steady state, it must be satisfied for all previous periods. Forwarding (16) by one period

and noticing that, with full depreciation of capital, KEt+1 = IEt , where I

Et is investment in

physical capital, we have

IEt+1 > ρEt+1IEt , ∀t. (17)

The inequality (17) is analogous to the necessary condition for the existence of bubbles in

the model of Abel et al. (1989) (AMSZ henceforth). Intuitively, housing bubbles are possible

if there exists a sequence of investment with costs exceeding the income flow it generates in

all periods.

32On the other hand, the incentive for entrepreneurs to hold bubbles does not depend on whether thereexists a wedge between the social and private returns to capital.

22

The inequality (17) implies that in a bubbly equilibrium, the young entrepreneurs would

voluntarily reduce their investment and hold housing in their portfolios, with the expectation

that the revenues from selling these bubbles will be no less than their forgone income from

capital investment. To see this point, note equation (9) implies that in the fundamental

equilibrium,

IEt+1 = (1 + ε) ρEt+1IEt , (18)

where ε ≡ ψ/[(1− ψ)α

(1 + β−1

)]− 1 > 0. Take the total derivative with respect to (18) ,

and let dIEt = −(PHt H − 0

); that is, the resources generated from a reduction in capital

investment (the left-hand side) are invested in housing (the right-hand side). Then, we have

the inequality PHt+1/P

Ht > ρEt+1. In other words, the rate of return to housing investment

would be greater than the rate of return to capital if entrepreneurial savings were all invested

in physical capital. As a consequence, expecting the inequality (17) to hold for all future

periods and thus a positive future demand for housing, the young entrepreneurs in period t

opt to divert savings into housing, which would raise the housing price PHt until the point

where the no-arbitrage condition PHt+1/P

Ht = ρEt+1 holds.

Our result is in contrast to that in the traditional bubble literature in two aspects.

First, the traditional bubble literature (e.g. the original AMSZ test) evaluates dynamic

(in)effi ciency based on the economy-wide rate of return to capital, rather than the rate of

return to capital for the marginal investors (i.e., productive entrepreneurs in our model).33

Second, in the traditional bubble literature, the social and private returns to capital facing

an agent are assumed the same. In contrast, they are not the same in our model because

of a wedge between the two. Thus, condition (16) needs to hold only with respect to the

private returns to E-firms’capital. This implies that an bubbly equilibrium may exist in our

model under dynamic effi ciency.

We now explore further the existence of bubbles under dynamic effi ciency. Dynamic

effi ciency implies that the steady-state MPKE in the fundamental equilibrium is larger

than the balanced growth rate

MPKE∗ |φE=1> (1 + z)(1 + ν). (19)

33As argued by Giglio and Severo (2012), looking at the average rate of return in the economy is notsuffi cient to judge the dynamic (in)effi ciency of market allocations, because there might be over-accumulationamong those who cannot park funds in productive assets (e.g., Martin and Ventura, 2012).

23

With (13) , condition (19) requires the following parameter restriction:

ψ < α(1 + β−1). (20)

Intuitively, the smaller ψ is, the smaller is the steady-state capital and the higher its marginal

product. Also, similar to standard OLG models, a higher α or a lower β makes the econ-

omy less likely to be dynamically ineffi cient. A combination of (15) and (20) gives further

parameter restrictions for bubbles to exist when the economy is dynamic effi cient:

α (1− ψ)(1 + β−1

)< ψ < α(1 + β−1). (21)

3.2.2 The Equilibrium Path

Given the existence of the bubble equilibrium, what ensures that the rational entrepreneurs

will choose their asset portfolios each period to reach such an equilibrium? Note that apart

from the two equilibrium sequences of housing prices (or investment) mentioned above, there

exist many other equilibrium paths along which the holding of the bubble asset per capita

converges to zero.34 It can be shown that the young entrepreneur’s portfolio share of savings

in housing assets is characterized by the following first-order difference equation

hEt+1 =hEt

1− hEt(1− ψ)α

(1 + β−1

)ψ

, (22)

where hEt ≡ 1− φEt . The first argument on the right side,hEt1−hEt

, is an increasing and convex

function of hEt . This equation implies that there are two steady states for hEt . At one steady

state, there is no bubble, hEt = 0 for all t. At the other, hEt = hE∗ = 1− (1−ψ)α(1+β−1)ψ

> 0,

so there is a bubble and the bubbly steady state is a saddle point. Moreover, for any initial

value hE0 ∈(0, hE∗

), the economy will converge to a bubble-less steady state: lim

t→∞hEt = 0.35

Only when hE0 = hE∗, is the bubble sustainable in the sense that the equilibrium path will

converge to the bubbly steady state in the long run.

Alternatively, we can show the dynamics of the system using a phase diagram of pHt and

34Such equilibrium paths, according to Tirole (1985), are called asymptotic bubble-less.35On the other hand, for any initial value hE0 > 1 − (1−ψ)α(1+β−1)

ψ ≡ hE0 , the system will explode andviolate the transversality condition, so it cannot be an equilibrium.

24

kEt . Appendix A shows that in this economy, there is a unique saddle path for pHt and k

Et .

For any initial level of an E-firm’s capital kE0 , when pH0 = pH0 ≡ hE∗ ψρE

(1+β−1)(1−ψ)αkE0 , the

economy will converge to the bubbly steady state at which ρE∗ = (1 + z) (1 + ν). For any

other pH0 =[0, pH0

), the economy converges to a steady state without bubbles. A unique

feature of our model is that the saddle path is linear during the transition stage due to its AK

feature. This generates a constant faster-than-income growth rate of the bubble (housing

prices).

To achieve the bubbly equilibrium, it is crucial for entrepreneurs in each period to expect

a particular sequence of housing prices that converge to the bubbly steady state. This

expectation is self-fulfilled in each period by the expected high future demand for housing,

which is rationalized by the fact that the future rate of capital returns, ρEt , will be suffi ciently

low in the post-transition stage. Under such an expectation, holding housing today can yield

high capital gains tomorrow even if housing has no intrinsic value. Accordingly, it is rational

for the currently young entrepreneurs to invest in housing even if they live only for a finite

number of periods.

Therefore, we assume that the economy starts with an initial portfolio share of housing

assets hE0 = 1 − (1−ψ)α(1+β−1)ψ

, which gives the following optimal portfolio share in physical

capital:

φEt =α(1 + β−1

)(1− ψ)

ψ,∀t. (23)

Equation (23) suggests that the entrepreneurs’portfolio share in housing assets is constant

along the transition path. This provides a testable implication of our model.

Although the short length of the household survey data in China (starting from 2011)

prevents a direct test of this implication on the share of entrepreneurial saving in housing,

the empirical evidence provided in Table 2 suggests that the share of real estate in total fixed

assets for non-real estate firms that invest in housing property (unrelated to their original

business) is very stable over time: about 14% to 15% between 2007 and 2013. Such a stable

pattern of portfolio share is consistent with our model’s prediction about the dynamics of

entrepreneurial portfolios in housing assets.

25

3.2.3 The Growth Rate of Housing Prices Relative to Output

Lemma 1 The growth rate of housing prices is equal to the growth rate of the output ofE-firms in both transition and post-transition stages.

PHt+1

PHt

=Y Et+1

Y Et

, ∀t. (24)

The intuition for Lemma 1 is as follows. In both the transition and post-transition stages,

the optimal portfolio choices by entrepreneurs will equalize the returns to capital investment

and the returns to bubbles through arbitrage. In this simple economy, the equilibrium portfo-

lio φEt is a constant, as the wedge between KEt+1 and ρ

Et K

Et in the fundamental equilibrium is

constant. This gives KEt+1 = ρEt K

Et in the bubbly equilibrium. Accordingly, the growth rate

of the total output of E-firm equals the rate of returns to capital for entrepreneurs, which in

turn equals the growth rate of housing prices according to the no-arbitrage condition.36

With Lemma 1, the following proposition captures the growth rate of housing prices

relative to that of aggregate output.

Proposition 1 Denoting ∆Xt as the growth rate of Xt, the growth rate of housing prices

exceeds that of aggregate output during the transition, and it converges to that of aggregate

output when the transition ends. Specifically,

∆ logPHt+1 = ∆ log Yt+1 + ∆ log

Y Et

Y Et + Y F

t

. (25)

Equation (25) implies that the gap between the growth rate of housing prices and that

of aggregate output equals the growth rate of the E-firms’output share in aggregate out-

put. During the transition, the aggregate output growth is a weighted average of the output

growth of the E-firms and F-firms. Since F-firms keep downsizing because of labor realloca-

tion, this sector’s output growth rate is less than that of E-firms, implying a lower growth

36More formally, the growth rate of total E-firm output is given by

Y Et+1Y Et

=Y Et+1KEt+1

KEt+1

KEt

KEt

Y Et=

ρEt+1(1− ψ)αρ

Et

(1− ψ)αρEt

= ρEt+1.

26

of the aggregate economy than that of E-firms.37 Therefore, housing prices, which increase

at the rate equal to that of the E-firms’output according to Lemma 1, will grow faster than

the growth rate of the economy at this stage. In the post-transition stage, the economy be-

comes essentially neoclassical: The growth rate of aggregate output equals the growth rate

of E-firms’total output. As a result, the housing price grows at the same rate of aggregate

output, even before reaching the steady state.

Furthermore, standard algebra shows that E-firms’output share in total output is given

by

logY Et

Y Et + Y F

t

= logNEt /Nt

1− ψ + ψNEt /Nt

. (26)

Therefore, together with Proposition 1, equation (26) implies that the growth rate of housing

prices relative to that of aggregate output depends positively on the growth rate of E-firms’

employment share, NEt /Nt. Note that during the transition, the growth rate of E-firms’

employment share is constant due to the constant growth rate of the E-sector’s capital stock

as implied by the AK feature.38 This implies a persistently higher growth rate of housing

prices than that of aggregate output. For a similar composition effect, the aggregate rate of

return to capital increases during the transition, despite the constant capital returns in both

E-firms and F-firms.39

The key to delivering a prolonged faster-than-GDP housing price growth rate in our model

economy is the presence of a prolonged transition stage featured by labor reallocation from

unproductive to productive (but financially constrained) firms. During this transition, the

entrepreneurs’high rate of return to capital is sustained by the existence of surplus labor in

the F-sector and is prolonged by borrowing constraints in the E-sector. Cheap surplus labor

is expected to be exhausted only after the transition ends when the diminishing returns to

37More formally, the growth rate of F-firms’total output follows

Y Ft+1Y Ft

=RKF

t+1/α

RKFt /α

=KFt+1

KFt

.

38More formally, the growth rate of E-sector’s employment share is

NEt+1/Nt+1NEt/Nt

=KEt+1/Nt+1

KEt (1 + z) /Nt=

ρEt(1 + z) (1 + ν)

.

39More formally, the aggregate rate of return to capital is computed as

ρt =ρEKE

t + ρFKF

t

KEt +K

Ft

=R

1− NEtNt

[1− χ ((1− ψ)χ)−

1α

] .

27

capital start to take effect. It is precisely this trajectory of returns to capital that entices the

productive agents (entrepreneurs) to invest in the housing market and become the marginal

buyers. The unproductive agents (workers or F-firms) can also invest in housing (which

yields much higher returns than bank deposits), but they will not be the marginal buyers.

This is in contrast to the results of Martin and Ventura (2012). In their paper, the

marginal buyers of bubble assets are the unproductive agents who face an extremely low

rate of return to capital (as in the traditional bubble literature). Consequently, their model

predicts a slower-than-GDP growth in the housing bubble, which is inconsistent with the

Chinese data. Moreover, in their paper, bubbles improve allocative effi ciency by crowding

in investment of the productive firms– which is again inconsistent with the Chinese data

in Section 2. In contrast, as the next section shows, bubbles in our model can worsen the

allocative effi ciency by crowding out investment of the productive firms– a serious concern

of the Chinese government for many years.

We also check the robustness of our model’s predictions for housing price growth by

extending our benchmark economy to alternative settings where (i) housing services are

valued; (ii) the economy consists of both labor-intensive and capital-intensive sectors such

that the labor share of SOEs does not converge to zero; (iii) entrepreneurs can borrow

against housing, and (iv) housing bubbles are stochastic. We show analytically that in each

of these alternative setups, the model robustly predicts that housing prices grow faster than

aggregate income during the economic transition.40

3.2.4 Economic Consequences of a Growing Bubble

An interesting issue is the normative implication of bubbles in our model. Because bubbles

can exist in our model without dynamic ineffi ciency, they may reduce, rather than increase,

social welfare. We now explore the welfare implications of growing bubbles in detail.

We first study the implications of bubbles for aggregate consumption in both the tran-

sition and post-transition stages. With condition (20) , the law of motion for capital (9)

implies that in the fundamental equilibrium, at each period t,

KEt+1 < MPKE

t ·KEt . (27)

In other words, investment in bubbles is not optimal for the social planner, despite the

incentive of entrepreneurs to invest in housing. The reason is simple: Given the suffi ciently

40These results are available upon request.

28

high marginal product of E-firms’capital, housing bubbles reduce the resource available for

aggregate consumption by crowding out productive investment.41

We now analyze the effect of bubbles on aggregate consumption. To allow bubbles to

reduce total entrepreneurial consumption, we further assume

ψ < α(1 + β−1) [ψ + α (1− ψ)] . (28)

Note that ψ + α (1− ψ) is the share of E-firms’output accrued to young and old entrepre-

neurs. Since ψ+ α (1− ψ) < 1, the inequality (28) is suffi cient for the condition of dynamic

effi ciency, (20) , to hold.42 To derive the effects of bubbles on each type of agent, we define

the period-t aggregate consumption of agent type-j ∈ {w,E} as cjt ≡ cj1,t + cj2,t(1 + ν)−1. We

have the following proposition:

Proposition 2 Given that (15) and (28) are both satisfied, a housing bubble reduces aggre-

gate consumption and welfare of both entrepreneurs and workers.

The intuition is as follows. In addition to the forgone capital returns, entrepreneurial

housing investment reduces the lifetime income of future entrepreneurs and, thus, generates

a negative externality on their consumption.43 It is easy to show that during the transi-

tion, since the rate of return to capital is constant, a reduction in lifetime income reduces

the entrepreneur’s lifetime utility. In Appendix B, we also show that bubbles reduce the

entrepreneurial lifetime utility at the steady state. For entrepreneurs born during the post-

transition stage, a suffi cient condition for welfare loss is α(1 + β−1

)> 1− α2.

Regarding the impact of housing bubbles on workers’consumption, note that the wage

rate, a constant along the transition, is unaffected by the presence of a bubble during the

transition. Hence, the welfare of workers during the transition is unaffected by the bubble.

However, when the transition ends, their lifetime utility decreases as a result of the housing

bubble. This is because the workers’wage income starts to depend positively on E-firms’

capital stock, while the rate of return to saving (the deposit rate) is still fixed.

The next question is whether it is desirable to burst a bubble once it exists, given that

bubbles crowd out productive investment. The answer is no. In our economy, the housing

41A similar wedge between social and private rates of return for capital occurs in the endogenous growthmodels of Grossman and Yanagawa (1993) and King and Ferguson (1993), in which the labor productivityof individual firms depends positively on the aggregate stock of capital.42A combination of (15) and (28) implies (1− ψ) (1− α) < ψ, which is guaranteed by mt ≥ wt, the

necessary condition for the young entrepreneur to work as a manager rather than a worker.43Given the initial capital stock and constant returns to capital, the permanent incomes of the old and

young entrepreneurs alive in the first period are unchanged when a housing bubble is introduced.

29

bubble serves as a store of value that enables the young entrepreneurs to finance retirement

consumption when old. Eliminating the bubble will therefore erode the retirement wealth of

the old entrepreneurs who happen to hold housing at the time the bubble bursts. To ensure

that no household is left worse off after the housing bubble bursts, the policymaker needs

to compensate these old entrepreneurs for their losses– say, by issuing government bonds to

the current-period young entrepreneurs. But the resources needed to compensate old entre-

preneurs are the same resources that would have been released by the young entrepreneurs

for capital accumulation. This implies that the policymaker is simply substituting another

form of a bubble for housing without crowding in productive investment. Such a policy

dilemma may explain why the Chinese government has been so reluctant to levy aggressive

property taxes to burst the housing bubble, despite its rapid growth and sheer size, as well

as its apparent crowding-out effects on capital investment. To support our argument, in

our quantitative exercise below, we show that a bursting housing bubble would reduce the

welfare for the majority of cohorts alive at the time of the burst.

4 Quantitative Analysis

This section brings the model to the data. To facilitate calibrations, we first extend our two-

period benchmark model to a multi-period model. In the model agents live for J periods,

are born with zero wealth, and cannot die with negative wealth. Workers supply one unit

of labor each period. They retire after JR years of work. Young entrepreneurs work for the

old entrepreneurs in the first JE periods of life. For simplicity, we assume that an age-j(j < JE − 1

)young entrepreneur can only make deposits in the bank with a fixed interest

rate R. From age JE−1 on, she can have a portfolio choice by purchasing housing or investing

in her own business. In this economy, we assume the capital depreciation rate δ < 1.

4.1 The Quantitative Multi-period Model

The F-firm’s problem is similar to that in the benchmark model:

maxkFt n

Ft

(kFt)α (

AtnFt

)1−α − wtnFt −RlkFt + (1− δ) kFt . (29)

For calibration purposes, we assume that lending to an F-firm is subject to a constant iceberg

cost ξ, which represents the intermediation cost. In equilibrium, the lending rate for F-firms

is Rl = R/ (1− ξ) .

30

An age-j old entrepreneur in time t solves the following problem:

π(kEj,t)

= maxnEj,t

(1− τ yt ) (1− ψ)(kEj,t)α (

AtχnEj,t

)1−α − wtnEj,t + (1− δ) kEj,t, (30)

where kEj,t and nEj,t denote the capital and labor deployed by an age-j old entrepreneur at

period t. We can derive the rate of returns for E-firms’capital as

ρEt ≡ π(kEj,t)/kEj,t = α (1− ψ) (1− τ yt )

1α [(1− α) (1− ψ)Atχ/wt]

1−αα + 1− δ. (31)

Note that, despite the heterogeneity in capital stock, the rate of return to capital is the same

for all entrepreneurs alive in period t under the Cobb-Douglas production function.

For calibration purposes, we assume that the production of E-firms is subject to a time-

varying output wedge τ yt . The purpose of introducing this wedge is to target the time

path of the private employment share in China.44 Such an output wedge may capture, in

reality, the preferential or distortionary policy toward private firms. For example, in the

early stage of privatization, the Chinese government provided various supports (e.g., credits,

tax deductions) to private firms, which encouraged their fast growth.45 This would show up

as an implicit output subsidy to E-firms (τ yt < 0). Over time, however, such preferential

policies have started to be replaced by various government policies that restrict the growth

of private firms (e.g., entry barriers for private firms into “strategic”industries and a heavy

tax burden), which had contributed to the so-called “Guo Jin Min Tui”(the state advances,

and the private sector retreats).46 This would show up in our model as an increase in the

value of τ yt . Since, in reality, government policies affect the overall profitability of private

firms, we assume that such an output wedge also applies to young entrepreneurs’managerial

compensation.

44Quantitatively, without the output wedge, housing prices still grow faster than GDP during the transitionstage. However, the increase of the private employment share will slow down. Accordingly, the simulatedhousing prices and housing price-to-GDP ratio grow at a slower rate than their benchmark counterparts.45For example, on June 29, 2002, the Ninth National People’s Congress Standing Committee passed the

Law of the People’s Republic of China on Promotion of Small and Medium-Sized Enterprise, which wasimplemented on January 1, 2003. In 2005, the State Council issued “Several Opinions of the State Councilon Encouraging, Supporting and Guiding the Development of Individual and Private Economy and OtherNon-Public Sectors of the Economy,”also called the “36 items for the non-public economy,”to support thedevelopment of private enterprises via preferential credit and tax policies.46For example, in 2007, the state government issued a document (the 39th Decree), which requests a

transition from preferential corporate income tax rates to legal tax rates. According to this document, thosewho enjoyed a 15% corporate income tax rate before 2008 would have tax rates of 18%, 20%, 22%, 24%, and25% for each year between 2008 and 2012, respectively.

31

For a worker of age i in period q, his problem for the remainder of his life is

maxJ∑j=i

βj−i log cwj,t (32)

subject to

cwj,t + swj,t = wt +Rswj−1,t−1, for j < JR (33)

cwj,t + swj,t = Rswj−1,t−1, for j ≥ JR (34)

swJ,t = 0, sw0,t−1 = 0, (35)

where the subscript t ≡ q + j − i is the calendar time for the age-i agent to become age j.An entrepreneur of age i in period q has the following consumption-saving problem

maxJ∑j=i

βj−i log cEj,t (36)

subject to

cEj,t + sEj,t = mt +RsEj−1,t−1, for j < JE − 1 (37)

cEj,t + sEj,t = ρEt sEj−1,t−1, for j ≥ JE − 1 (38)

sEj,t ≥ 0 for j ≥ JE − 1 (39)

sEJ,t = 0, sE0,t−1 = 0. (40)

Here again, for the no-arbitrage condition to hold, we assume that the inner solution of

entrepreneurial portfolio choice exists. Given the savings, sEj,t, the age-j entrepreneur at

period t then makes the portfolio choice φEj,t.

Proposition 3 There exists an equilibrium in which all entrepreneurs alive in period t will

invest the same share of wealth in housing; that is, φEj,t = φEt , for j ∈[JE − 1, J − 1

].

Proposition 3 allows us to derive the following equations for aggregate capital and housing

stock in equilibrium.

32

KEt+1 = φEt

J−1∑j=JE−1

NEj,ts

Ej,t, (41)

PHt H

Et =

(1− φEt

) J−1∑j=JE−1

NEj,ts

Ej,t, (42)

where NEj,t denotes the number of entrepreneurs of age j at period t. Therefore, we can solve

the aggregate labor demand and portfolio choices by aggregation. Appendix C describes the

numerical algorithm to solve for the calibrated economy.

4.2 Calibration

We use data from the NBSC to calibrate the model. The model economy starts in 1998,

when China started to privatize its SOEs. Each period in our model corresponds to one

calendar year.

Consider the first set of parameters, whose values are set exogenously. Agents in our

model enter the economy at age 22 and live for 50 years. This is consistent with an average

life expectancy for males and females of 71.4 years according to the 2000 Chinese Population

Census. Workers retire after 30 years. The population growth rate is set to ν = 0.03,

consistent with the average urban population growth rate in China during 2002-2012.47

In terms of technology parameters, the capital income share is set to α = 0.5, consistent

with Bai, Hsieh, and Qian (2006).48 The capital depreciation rate is set to δ = 0.1, which is

the average depreciation rate between 1998 and 2012, computed using the method of Bai,

Hsieh, and Qian (2006). The land supply is normalized to H = 1, and the bank deposit rate

is set to R = 1.0175, following SSZ (2011). Finally, the initial assets of the workers and

retirees are set to be the same as the corresponding wealth in an initial steady state with

only F-firms.

Now we turn to the second set of parameters, whose values are set endogenously to target

certain data moments. We calibrate β = 0.994 to match the average aggregate saving rate

47Urban population growth could be endogenously driven by rural-urban migration, which in turn couldbe an outcome of labor reallocation from SOEs to POEs. We view this as an interesting extension for futureresearch.48Since in our model housing does not provide services and is in fixed supply, our measured capital stock

corresponds to the concept of total reproducible capital stock, which we constructed following the methodof Bai, Hsieh, and Qian (2006).

33

between 1998 and 2012 of 40%. We then set ψ = 0.53 to match the aggregate rate of returns

to capital at 1998, which is 20%. Following SSZ, we calibrate the productivity parameter

of E-firms to be χ = 5.64 to match the following moment: The capital-to-output ratio of

Chinese SOEs is 2.65 times that of domestic private firms. The iceberg cost ξ is set to 0.0693

to match the marginal product of capital (MPK) for SOEs to be 0.093. The rate of labor-

augmented technological growth is set to z = 3.8% to match the average growth rate of GDP

of 10% during 1998-2012.

The initial entrepreneurial wealth is set to match an initial employment share of private

firms at 1998. According to NBSC data, the employment share of private firms (DPE +

FE) in total employment is 17% in 1998. Accordingly, the initial life-cycle distribution of

wealth for managers and entrepreneurs is a scaled-down version of the life-cycle distribution

of wealth for workers in the initial steady state. For the time path of output wedges, we

assume a linear pattern between τ y1998 and τ y2012, such that τyt = τ y2012 − (2012− t)κ for

1998 ≤ t ≤ 2012. For t ≥ 2013, we assume τ yt = 0. We then calibrate τ y2012 and κ to best fit

the trajectory of the private employment share between 1998 and 2011. This gives κ = 0.027,

τ y2012 = 0.01.

4.3 Main Results

To assess the model’s performance, we compare the simulated housing prices with both the

annualized constant-quality housing price indices between 2006 and 2010 and the annual

constant-quality national-level land price indices by Wu, Gyourko, and Deng (2012).49 The

land price data cover the period of 2004-2012 and were updated on Gyourko’s webpage.

Since the land price tracks the housing price closely (see Figure 1), we view the land price

as a good proxy for the housing price for those years with missing housing price data. To

illustrate the growth rate of the housing price relative to that of GDP, we also construct

the ratio of housing prices to GDP in both the model and the data. We then normalize the

simulated and actual housing prices and housing price-to-GDP ratio in 2004 to 1.

Figure 6 shows the main predictions of the model, together with their data counterparts.

In Panel A, we see that the simulated housing prices replicate the actual data fairly well

until 2011, with an average growth rate of 19% between 2004 and 2011. The over-prediction

49The two most authoritative sources of housing price data are Wu, Gyourko, and Deng (2014) and Fang etal. (2015). Neither of these two data sources allow us to go back earlier than 2003. Other publicly availabledata for housing prices, such as the NBS average price index (total revenue of housing sales/floor area ofhousing sales), are severely biased downward (Wu, Deng, and Liu, 2014); hence, they are not reliable for ourpurposes. The year 2004 may be a good starting point for another reason: Public auctions or bidding forland prices were non-existent before 2002.

34

of housing prices in 2012 may be due to the fact that since 2010, the Chinese government has

adopted several policies to control housing prices, from which our model is abstracted. Panel

B shows that the simulated housing price-to-GDP ratio increases from 1 in 2004 to 1.77 in

2012, or an average of 7.43% per year. Hence, our model can replicate the magnitude of the

increase in housing prices relative to GDP reasonably well. We view this result as further

support of our mechanism for the housing price dynamics in China, since labor reallocation

from F-firms to E-firms is key to delivering a sustained high return to E-firms’capital, not

only in absolute terms, but also relative to the growth rate of aggregate output.

Panel C of Figure 6 shows that our model can closely match the dynamics of the private

employment share. Note that as time approaches the year 2012, the increase of the private

employment share starts to slowdown. This is because entrepreneurs slow their accumulation

of physical capital in anticipation of an increase in implicit output distortion.

In Panel D of Figure 6, the aggregate rate of returns to capital is persistently high between

1998 and 2012. It starts to decline around 2008, which coincides with the turning point of

the data. Two opposite effects in the calibrated economy drive the dynamics. On the one

hand, the increase of the private employment share increases the average returns to capital,

thanks to a higher E-firm rate of return to capital. On the other, the increase in implicit

output distortion on E-firms during this period tends to reduce their net return to capital.

Panel E of Figure 6 shows that the aggregate output growth in our model replicates

China’s GDP growth reasonably well: It is sustained around 10% between 1998 and 2012.

Again, the observed hump shape of output growth rates is due to the aforementioned two

opposite effects.

Panel F of Figure 6 plots the dynamics of aggregate TFP. Between 1998 and 2006, the

average TFP growth rate is 6.13 percent. This is in line with the estimation of Brandt,

Van Biesebroeck, and Zhang (2009), who report an estimate for manufacturing sector TFP

growth of 6.1% to 7.7% during 1998-2006. Resource reallocation contributes 4.23% to annual

TFP growth. Therefore, 69% of the TFP growth between 1998 and 2006 in our model is

due to resource reallocation, which is broadly consistent with the findings of Brandt, Van

Biesebroeck, and Zhang (2009). A falling TFP growth rate in the second half of our sample

period is due to an increase in the implicit output distortion toward E-firms, which, in turn,

slows the pace of labor reallocation.

4.4 Counterfactual Experiments

We now conduct several counterfactual experiments to shed additional light on the structure

of our model.

35

Heterogeneity. A standard representative-agent neoclassical growth model also features

a transitional period of capital accumulation before reaching the steady state, along which

the MPK declines gradually. Would this declining MPK along the neoclassical transition

generate a faster-than-GDP growth in housing prices, everything else equal? The answer

is no. To illustrate this, we exclude F-firms in our model so the counterfactual economy is

essentially neoclassical with only E-firms and without the transition stage featuring “surplus”

labor and resource reallocation– the focus of our model. In this counterfactual economy, the

parameters χ and kEt measure the aggregate, rather than E-firm-specific, productivity and

capital stock, respectively. Therefore, we set kE1 to be the same as the initial aggregate capital

stock in the benchmark economy. We then recalibrate χ to target an initial aggregate rate

of return to capital of 0.20. We keep all other parameters the same as in our benchmark

economy. Figure 7 shows the simulated results in this counterfactual economy, together with

their counterparts in the original model. Without firm heterogeneity, the private employment

share always equals 100% (Panel C). Panel A shows that in this counterfactual economy,

housing prices grow significantly slower than the benchmark counterparts. Two reasons

explain this: First, in this counterfactual economy, the growth rate of housing prices equals

the aggregate rate of return to capital. Second, the aggregate rate of return to capital

falls over time along with capital accumulation (Panel D). In contrast, in our benchmark

economy, the rate of housing price growth equals the rate of return to E-firm’s capital, and

the AK feature of E-firms helps to sustain the high capital returns during the transition.

Accordingly, in this counterfactual economy, the housing price relative to GDP is essentially

flat (Panel B), despite a declining output growth rate (Panel E). Intuitively, without firm

heterogeneity, the dynamics of aggregate output growth closely track the dynamics of the

aggregate return to capital, which implies that housing prices grow at a rate similar to that

of aggregate output.50

The Crowding-Out Effects of the Housing Bubble. We now explore the normative impli-

cations of housing bubbles. To this end, we shut down entrepreneurs’access to the housing

bubble by setting φEt = 1 for all t. Accordingly, without demand the housing prices will

always equal zero. All parameters remain the same as in the original calibration. Figure 8

plots the transition path for both the counterfactural and the original economies. Panel A

shows that without housing bubbles, the private employment share rises much faster. For ex-

ample, by 2011, the private employment share is around 77%, 9% higher than the benchmark

50When physical capital is not fully depreciated, the growth rate of E-firms’total output will be somehowless than the aggregate or entrepreneurs’returns to capital, because the growth rate of entrepreneurs’wealthis decreasing over time before the economy reaches the steady state.

36

counterpart. This implies that the presence of a housing bubble prolongs the economic tran-

sition. Panel B shows that without housing bubbles, aggregate output grows faster between

1998 and 2011, with an average growth rate of around 11%. Accordingly, the steady-state

aggregate output is 6.23% higher than its counterpart in the bubbly equilibrium. Panel C

shows a similar pattern for the TFP growth rate. Between 1998 and 2011, TFP grows at an

average rate of 6.05% per year, in contrast to the rate of 5.51% in our benchmark economy.

Such a disparity suggests that housing bubbles exacerbate resource misallocation by crowd-

ing out productive investment, slowing labor reallocation from unproductive firms (F-firms)

to productive firms (E-firms), thus resulting in permanently lower aggregate productivity

and effi ciency. Panel D suggests a significant welfare loss due to the presence of a housing

bubble. Between 1998 and 2012, aggregate consumption would be 6.35% higher without the

housing bubble. Even at steady state, aggregate consumption is 3.75% higher in the fun-

damental equilibrium. Intuitively, by crowding out productive capital investment, housing

bubbles reduce the permanent incomes of future cohorts via both managers’compensation

and the wage rate.

The Housing Bubble Burst. Since the bubble is welfare reducing, it is tempting to con-

clude that it is welfare improving to burst the bubble after it emerges. This intuition is not

entirely correct. To show this, we conduct an experiment with an unexpected bubble burst

in year 2012 in our model (the last period of our data sample) and compute the welfare ef-

fects on both workers and entrepreneurs alive in 2012. Implicitly, the welfare results in such

a counterfactual experiment could be used in a political economy model under a majority

voting scheme among existing cohorts regarding whether to burst the housing bubble. The

results of the experiment are presented in Figure 9. Interestingly, all workers born before

1990 in our economy (which corresponds to cohorts born in year 1969 or earlier in the data)

do not experience welfare change. This is because these cohorts of workers retire before the

bubble burst. Hence, their lifetime income, which is the present value of the wage rate, is

unchanged. Workers born after 1990 experience welfare gains because they enjoy an increase

in the wage rate during their working periods when the economy enters the post-transition

stage after the bubble bursts. The younger workers are, the higher the welfare gain due to

their longer working period.

In contrast, all entrepreneurs alive in 2012 suffer welfare losses. Specifically, the old

entrepreneurs (aged 26 and older in our model) not only suffer a loss of housing wealth, but

also miss the increase in managerial compensation due to the burst of the bubble. For the

young entrepreneurs, two offsetting welfare effects are present. On the one hand, the burst

of the bubble increases the compensation of the young entrepreneurs for their remaining

37

working periods as managers, thus increasing their lifetime income. On the other hand, the

event decreases the rate of return to E-firms’physical capital in the post-transition stage

(which starts in the year 2019 in our model). Our quantitative results suggest that the

welfare losses dominate the welfare gains for the young entrepreneurs alive in 2012.

To sum up, the majority of agents who are currently alive (workers plus entrepreneurs)

will not benefit from the bubble’s burst. This is despite the fact that in the long run,

all newborn entrepreneurs and workers enjoy welfare gain. This welfare result provides a

rationalization for why the Chinese government has been reluctant to burst the housing

bubble, even though doing so is welfare improving in the long run.

4.5 Further Discussions of Model Implications

While the focus of our paper is China, our model can shed light on the occurrence of housing

bubbles in other emerging economies during their rapid-growth transition periods. The

highlight of our theory is that economic transitions driven by massive resource reallocation

must eventually end and that the associated high capital returns are thus unsustainable in

the long run. Such transition economies are prone to bubbles because such a dynamic path of

capital returns can induce even the most productive agents in the economy to seek alternative

stores of value for their rapidly growing wealth. In financially backward economies without

sophisticated regulatory institutions, land or the housing market often becomes the natural

target of speculative investment. Indeed, in other East Asian economies during their earlier

stages of industrialization and rapid economic growth, such as South Korea and Taiwan in

the 1980s, intersectoral labor reallocations from agriculture to manufacturing (or the service

sector) contributed importantly to their fast economic growth, and the high capital returns

sustained by resource reallocation have been accompanied simultaneously by faster-than-

income growing housing prices.51 Also, Vietnam has experienced a transition stage similar

to that in China. Therefore, a brief analysis of these economies’housing booms serves as a

useful examination of the relevance of our theory for other emerging countries.

In South Korea, land/housing prices almost tripled during 1985-1991, with an annual

growth rate of 21.5% on average.52 This is in contrast to an average real GDP growth rate

of 12.5% during the same period. Interestingly, this housing boom coincided with important

51SSZ (2011) emphasize the resource reallocation to financially constrained private firms within the man-ufacturing sector as a key reason for the coexistence of acceleration of productivity growth and a foreignsurplus in Korea and Taiwan in the 1980s. We view the intersectoral labor reallocation as essential for thehousing booms experienced in these two countries during the 1980s.52See Koo and Park (1994, Table 3.9) and Kim and Lee (2000). Also, according to these two studies,

between 1980 and 1985, land prices increased by only 60%. After 1992, both land and housing prices leveledoff until the 1997-98 financial crisis.

38

structural changes in the Korean economy. In the 1980s, Korea experienced a massive

reallocation of labor from agricultural to other sectors. The share of agricultural employment

dropped by 20% between 1980 and 1992, compared with a mere 6% drop between 1992 and

2007 (Lee, 2010). Labor costs had been rising significantly since the mid-1980s, reflecting a

pending shortage of labor (Smith, 2000, Figure 3.3). While the rate of increase slowed by the

early 1990s, the real average monthly earnings in manufacturing still grew by an average of

7.8 per year between 1992 and 1996, while productivity growth lagged. This increase in labor

costs increasingly undermined Korean firms’competitiveness, which led to a rapid increase

in relative export prices during this period (Smith, 2000, Figure 3.2). Such an increase in

labor costs is consistent with the dynamics of the rate of return to capital for Korea. As

shown by Panel A of Figure 10, the rate of return to capital was very high and increased for

most of the 1980s before it started to fall in the late 1980s.53

Similar to South Korea’s experiences, the housing boom in Taiwan occurred during a

time of massive labor reallocation and fast economic growth. According to Koo and Park

(1994), Taiwan witnessed a sharp increase in land prices in the second half of the 1980s.

Accordingly, average housing prices in the Taipei area more than quadrupled from late 1986

to early 1990 (implying a more than 40% annual growth rate of housing price during this

period).54 During the same period, real GDP grew at an annual rate of 9.1%. At the micro

level, Taiwan experienced a fast reallocation of labor from agriculture to manufacturing and

service sectors since the 1970s. The share of agricultural employment dropped from 25% in

1978 to 13% in 1989. A labor shortage had gradually become apparent in the manufacturing

sector since the late 1970s and more so after the mid-1980s. Labor costs rose as a result of

this labor shortage. The average monthly real wage, which increased by 6.5% per year during

1981-1986, increased by 11.4% per year between 1986 and 1990.55 Accordingly, Panel B of

Figure 11 shows that Taiwan’s returns to capital peaked in 1986-87 and declined thereafter.

Similar to China, Vietnam has witnessed a massive labor reallocation from SOEs toward

the private sector in the past decade following a series of reforms (e.g., the establishment

of the 2000 Enterprise Law). For example, within the manufacturing sector, the share of

53Nugent and Yhee (2002, Table 6) obtained a similar finding for the dynamics of capital productivity,especially for small and medium-sized enterprises. Specifically, capital productivity, measured by the ratio ofgross value added to total assets, is more than 35 percent for small and medium-sized enterprises and morethan 24 percent for large enterprises during 1985-1991. This is in contrast to a declining pattern of capitalproductivity for both types of firms between 1992 and 1997.54See Chen (2001, Table 1) for the data on the real housing price growth rate for Taipei during the late

1980s, and Tsai and Peng (2011) for evidence on the housing market boom for other major cities in Taiwanduring this period.55Similar to Korea, Taiwan also experienced a sharp increase in the relative export prices in the second

half of the 1980s (Smith 2000, Figure 3.2).

39

workers employed by SOEs has declined from 0.305 in 1999 to 0.089 in 2009, while the share

of workers employed by foreign-owned firms has increased from 0.052 to 0.224.56 Associated

with Vietnam’s structural change is its fast economic growth. According to the International

Monetary Fund, Vietnam’s average GDP growth was 7.2% between 2000 and 2010– one of

the fastest-growing economies in the world during this period.

Along with its economic transition, Vietnam’s real estate market has undergone remark-

able changes in recent years. In 2003, the Vietnamese government enacted the Law on Land.

This law casts the most significant reform of legal property rights in Vietnam’s history and

paves the way for market-driven real estate prices in Vietnam. The real estate market in

Vietnam experienced a boom between 2007 and 2010. For example, housing prices increased

by 200% between 2007 and the first half of 2008, and medium- to high-quality condominiums

became one of the hottest asset markets, second only to Vietnam’s booming stock market.

The incredible rise in housing prices, nonetheless, was believed to be the result of significant

speculation rather than by changes in the fundamentals. Since the beginning of 2011, the

real estate market in Vietnam has suffered huge losses in market value. Housing prices have

dropped by 40 percent on average since then.

Therefore, despite important cultural and institutional differences, these three emerging

economies all shared some common features in their development paths similar to China’s

recent experience. Specifically, all three economies experienced faster-than-GDP growth

in housing prices despite high capital returns during their respective economic transitions.

Moreover, for both Korea and Taiwan, the completion of the transition process eventually

led to rising labor costs and the cooling of housing bubbles. These features are consistent

with the predictions of our theory.

5 Conclusion

This paper provides a framework to explain the coexistence of three paradoxical features of

the great housing boom in China– the persistently faster-than-income growth rates of hous-

ing prices, the phenomenal capital returns, and the exceptional vacancy rates across major

Chinese cities (the ghost-town phenomenon). Our theory suggests that China’s unprece-

dented income growth is not the full story behind the great housing boom. The decade-long

housing boom contains a rational bubble arising naturally from China’s economic transition,

which is featured by labor reallocation from the traditional low-productivity sector to the

56See McCaig and Pavcnik (2013, Table 5). According to them, another important structural change duringthis period is the acceleration of reallocation of labor from the agricultural sector to the manufacturing andservice sectors.

40

newly emerging high-productivity sector. Such labor reallocation sustains a very high rate

of returns to capital in the emerging sector. Yet, the high capital returns will eventually

come to an end when the surplus labor is depleted. Hence, rational expectations of high

demand for alternative stores of value in the future can induce even the most productive

current agents to speculate in the housing market, creating a self-fulfilling housing bubble

that can grow much faster than aggregate income despite high capital returns. The model’s

predictions are thus consistent (qualitatively and quantitatively) not only with China’s broad

pattern of economic growth but also with the three paradoxical features of the great housing

boom. We also show that such a growing housing bubble can crowd out productive capital

investment, thus prolonging the economic transition and reducing social welfare.

A number of simplifying assumptions make our model tractable. For example, in our

model housing does not provide utility services and workers do not participate in the housing

market. Although we have argued that such omissions should not affect our main results, a

richer model with both workers and entrepreneurs speculating in the housing market would

enrich the welfare implications of growing housing bubbles. For example, a growing housing

bubble distorts homeowners’life-cycle consumption patterns under borrowing constraints by

forcing people to save excessively when young to enter the housing market. Furthermore,

the rapidly rising housing prices tend to worsen wealth inequalities across income classes,

as the housing price growth is driven largely by the high- and upper-middle-income classes

that have enjoyed the most rapid income growth during China’s economic development. In

contrast, under borrowing constraints more and more low-income households are excluded

from the housing market because their income growth lags behind housing price growth.

Moreover, our model abstracts from several institutional details of China’s housing and land

markets (e.g., a local government’s heavy reliance on revenue from land sales), which, we

believe, might also be a contributing factor to the size (but not growth rate) of China’s

housing bubble. These are all important issues for our future research.

Despite its simplicity, a calibrated version of our model quantitatively matches the growth

dynamics of housing prices and other salient features of the recent Chinese experience reason-

ably well. We therefore view our model as a useful starting point to study the macroeconomic

implications of the growing housing bubble in China. For example, a growing housing bub-

ble reduces the private sector’s incentive to innovate. Because of the relatively low risk,

low entry costs, low technology, and high profits in housing investment, the housing bub-

ble has enticed many productive and high-tech firms in China to reallocate resources from

research and development to the real estate market. In an economy in transition from a

labor-intensive economy to a capital-intensive economy, such resource misallocation can be

very costly: It may substantially prolong China’s economic transition and reduce China’s

41

TFP growth, especially when its population is aging fast and labor costs are rapidly ris-

ing. We plan to empirically validate and quantify such resource misallocation within our

framework in future works.

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45

Tables and Figures

Table 1. Excess Housing Price Growth and Capital Returns

Variable (1) (2) (3)

Private capital returns 0.8153(0.1725)

∗∗∗ 0.7101(0.1737)

∗∗∗

SOE capital returns 0.7573(0.2676)

∗∗∗ 0.5091∗∗(0.2124)

Observations 139 139 139

R2 0.2349 0.1111 0.2819

Note: *** Significant at the 1% level. ** Significant at the 5% level. Numbers in parentheses

are standard errors. This table reports the results from our fixed-effects panel regression with

excess housing price growth as the dependent variable and private and/or SOE capital returns as

the independent variables. The estimation uses the robust or sandwich estimator of variance. The

data are a balanced panel covering 35 major cities in China between 2006:Q1 and 2010:Q4.

Source: The data for the housing prices of the 35 cities are from Wu, Deng, and Liu (2014). The

data for disposable income growth for the 35 cities are from the statistical communiques, various

issues. The data for capital returns for various provinces and municipalities directly governed by

the central government are from the China Statistical Yearbook (CSY), various issues.

Table 2. Summary Statistics for Firms with Investment Property

Total Number Firms % of Firms with Average

Year of Firms with IP IP IP/(IP+PPE)

2007 1373 609 44.36% 16.03%

2008 1489 662 44.46% 15.64%

2009 1534 699 45.57% 15.54%

2010 1681 732 43.55% 15.57%

2011 2027 858 42.33% 14.46%

2012 2254 872 38.69% 13.86%

2013 2249 926 41.17% 13.35%

Note: IP denotes Investment Property. This table provides the summary statics for non-real

estate publicly listed firms holding property assets for investment purposes. We restrict our sample

to firms that have been traded for at least two years on the China A-share stock market over the

period of 2007-2013. We exclude firms in the real estate and construction sectors.

Source: The firm level data are from CSMAR and authors’calculation.

46

Table 3. Returns to Capital and Ownership Structure

(1) (2) (3)

Variable measure 1 measure 2 measure 3

State ownership −1.02734(−9.32)

∗∗∗ −0.13056(−1.64)

∗ −0.49989(−8.98)

∗∗∗

Observations 10957 10957 10957

R2 0.2573 0.2521 0.2547

Note: This table reports the estimated coeffi cient in a regression of capita returns against three

measures of state ownership and four one-digit industry dummies. Measure 1 is the state-owned

stock share, measures 2 and 3 are state-ownership dummies with value of 1 if a firm’s state-owned

stock share exceeds 50% and 25%, respectively. *** Significant at the 1% level. ** Significant at

the 5% level. * Significant at the 10% level.

Table 4. Correlation between Housing Price Growth and Fixed Investment Growth

Nationwide

Time Real Estate Investment Other Investment

Current 0.5255∗∗ -0.3212∗∗

t− 1 0.4765∗∗ -0.4046∗∗

t− 2 0.4115∗∗ -0.4499∗∗

t− 3 0.3320∗∗ -0.5025∗∗

t− 4 0.2710∗∗ -0.5467∗∗

t− 5 0.2025 -0.5438∗∗

t− 6 0.1288 -0.5171∗∗

Source: The aggregate monthly house price data from January 2006 to December 2011 are from

Wu, Deng, and Liu (2014). The corresponding monthly investment data are from the CSY (various

issues). To remove seasonality, the growth rates for housing prices and investment are computed

as the growth rate over the same month of the previous year. ∗∗Significant at the 5% level.

47

2004 2005 2006 2007 2008 2009 2010 2011 2012 201350

100

150

200

250

300

350

400

y ear

2004

q1=1

00

Hedonic Housing/Land Price

housing priceland price

Figure 1. Housing/Land Prices in China

Source: The hedonic house price data are from Wu, Deng, and Liu (2014), and the hedonic land

price data are from Wu, Gyourko, and Deng (2012, downloadable from

http://real.wharton.upenn.edu/~gyourko/chineselandpriceindex.html.)

48

4 6 8 10 12 14 160

5

10

15

20

25

30

35

Real av erage annual growth rate f or disposable income, %

Rea

l ave

rage

 ann

ual g

row

th ra

te fo

r hed

onic

 hou

sing

 Pric

e, %

Beijing

Fuzhou

Haikou

ShanghaiXiamen

Chongqing

Guangzhou

Nanjing

Wulumuqi

Shenzhen

Ningbo HangzhouQingdao

ChangshaZhengzhouGuiy angLanzhou

Tianjin

Xining

Taiy uan

NanchangShijiazhuang

Jinan

Chengdu

Hef ei Sheny angHuhehaote

WuhanY inchuan

NanningDalian

KumingHaerbin

XianChangchun

Housing Price Growth v s Income Growth

Figure 2. Growth Rate of Housing Prices and Aggregate Income across Major Cities in

China

Source: The hedonic house price data for 35 major cities are from Wu, Deng, and Liu (2014).

The growth of disposable income is computed by the authors based on the growth rate of real

disposable income and the growth rate of the urban-residing population from various issues of the

statistics communiqués for different cities.

49

1998 2000 2002 2004 2006 2008 2010 20120

5

10

15

20

25

30

35

year

perc

ent

Panel A: Return to Capital

1998 2000 2002 2004 2006 2008 20100

10

20

30

40

50

60

70

80

year

perc

ent

Panel B: Private Employment Share

BaselineAfter­tax, Excluding H

DPE/(DPE+SOE)(DPE+FE)/(DPE+FE+SOE+COE)

Figure 3. Returns to Capital and Labor Reallocation

Note: DPE, domestic private enterprises; FE, foreign enterprises; SOE; state-owned enterprises;

COE, collectively owned enterprises.

Source: In Panel A, the rate of return to capital for various years is computed by the authors

using the approach of Bai, Hsieh, and Qian (2006) and data from the CSY (various issues). The

line with circles refers to the gross rate of return to capital, and the dash-dotted line refers to the

after-tax return to capital excluding urban residential housing. In Panel B, the private employment

shares are computed by the authors using data from the CSY (various issues).

50

1996 1998 2000 2002 2004 2006 2008 201018.2

18.4

18.6

18.8

19

19.2

19.4

19.6

year

milli

ons 

of a

cres

Figure 4. Total Amount of Arable Land

Source: CSY (various issues).

51

1998 2000 2002 2004 2006 2008 2010 20120

1

2

3

4

5

6

7

8

9

year

perc

ent

Deposit RateLending Rate

Figure 5. China’s One-Year Benchmark Nominal Interest Rates

Source: CEIC database.

52

2004 2006 2008 2010 20121

2

3

4

5

year

Y04=

1

Panel A: Housing Price

BenchmarkLand PriceHousing Price

2004 2006 2008 2010 2012

1

1.5

2

year

Y04=

1

Panel B: Housing Price/GDP Ratio

2000 2005 20100

20

40

60

80

year

perc

ent

Panel C: Private Employment Share

2000 2005 20100

10

20

30

40

year

perc

ent

Panel D: Returns to Capital

2000 2005 20100

5

10

15

20

year

perc

ent

Panel E: Aggregate Output Grow th

2000 2005 20100

5

10

year

perc

ent

Panel F: TFP Grow th Rate

Figure 6. Transition in the Multiperiod Calibrated Economy

Note: This figure shows the evolution of key variables during and after transition of the cal-

ibrated economy. The solid and dash-dotted lines refer to the simulated results from the model

and the data, respectively. In Panel A, the plus sign refers to annualized housing price data from

Wu, Deng, and Lin (2014), whereas the dash-dotted line refers to annual land price data from Wu,

Gyourko, and Deng (2012). Both the simulated housing price data and actual land price data are

normalized to 1 in 2004. The housing price data in 2006 are normalized to equal the normalized

actual land price data in 2006.

53

2004 2006 2008 2010 2012

1

1.5

2

year

2004

=1

Panel B: Housing Price/GDP Ratio

2004 2006 2008 2010 20121

2

3

4

5

year

2004

=1

Panel A: Housing Price

BenchmarkNo F­Firm

2000 2005 20100

50

100

year

perc

ent

Panel C: Private Employment Share

2000 2005 20100

10

20

30

40

year

perc

ent

Panel D: Returns to Capital

2000 2002 2004 2006 2008 20100

5

10

15

20

year

perc

ent

Panel E: Aggregate Output Grow th Rate

2000 2005 20100

5

10

year

perc

ent

Panel F: TFP Grow th Rate

Figure 7. The Role of Firm Heterogeneity in the Calibrated Economy

Note: The figure shows the evolution of key variables in the calibrated economy (solid line) and

the counterfactual economy in which there are no F-firms (dash-dotted line).

54

2000 2005 20100

20

40

60

80

year

perc

ent

Panel A: Private Employment Share

BenchmarkNo Bubble

2000 2005 20108

9

10

11

12

year

perc

ent

Panel B: Aggregate Output Grow th Rate

2000 2005 20100

2

4

6

8

year

perc

ent

Panel C: TFP Grow th Rate

2000 2005 20100.6

0.7

0.8

0.9

1

1.1

year

Panel D: Aggregate Consumption

Figure 8. The Welfare Effects of Housing Bubbles in the Calibrated Economy

Note: The figure shows the evolution of key variables in the calibrated economy (solid line) and

the counterfactual economy in which there are no housing bubbles (dash-dotted line).

55

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010­15

­10

­5

0

5

10

y ear of  birth

perc

enta

ge c

hang

e in

 wel

fare

EntrepreneurWorker

Figure 9. Welfare Effects of Bubble Burst in 2012

Note: This figure shows the welfare effects of an unexpected burst of a housing bubble in 2012

for all cohorts alive at the time of the burst.

56

1980 1985 1990 1995 20000.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3Panel A: Korea

year

Mar

gina

l Ret

urn 

to C

apita

l

1980 1985 1990 1995 20000.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.3Panel B: Taiwan

Mar

gina

l Ret

urn 

to C

apita

l

y ear

Figure 10: The Return to Capital for Korea and Taiwan

Note: The figures show the rate of return to capital for Korea and Taiwan during housing

bubbles in these two countries.

Source: The rate of return to capital for various years is computed by the authors as (1−laborsharet)× Yt/Kt−δt. The original source of GDP, capital stock, and capital depreciation rate datais the Penn World Table (8.0). Yt is output-side real GDP at current PPPs in millions 2005US$,

Kt is capital stock at current PPPs in millions 2005US$, and δt is average depreciation rate of the

capital stock. We convert Yt and Kt into the local currency when computing the return to capital

for individual countries.

57

APPENDIXES (not for publication)

A. Phase Diagram of the Benchmark EconomyThe dynamic system can be described by two difference equations in the detrended E-firm’s

capital and housing price:

kEt+1 (1 + z) (1 + ν) + pHt H =ψ

1 + β−1

(kEt

)α (χnEt

)1−α(A1)

pHt+1 (1 + z) (1 + ν) = ρEt+1pHt (A2)

where

ρEt+1 =

ρE if kEt ≤ kE

α (1− ψ)(kEt+1/χ

)α−1if kEt > kE

,

and kE ≡ χ/{

[(1− ψ)χ]1α (R/α)

11−α

}is the minimum level of an E-firm’s capital under

which nEt = 1. Accordingly, the constant kE locus (kEt+1 = kEt ) is characterized by the

following step function:

pHt =

[

ρEψ

(1−ψ)α(1+β−1)− (1 + z) (1 + ν)

]kEt if kEt < kE

ψ1+β−1

(kEt

)αχ1−α − kEt (1 + z) (1 + ν) if kEt ≥ kE

. (A3)

Obviously, when kEt < kE, the constant kE locus is an upward-sloping straight line due to

the AK feature of E-firms’return to capital during the transition stage. When kEt ≥ kE, the

constant kE locus looks like their counterpart in the standard neoclassical economy and is

hump-shaped. Moreover, from (A1) and (A2) , the constant pH locus is characterized by

pHt =ψ

1 + β−1

(kEt

)αχ1−α − (1 + z) (1 + ν) ρE−1 ((1 + z) (1 + ν)) (A4)

where ρE−1 is the inverse function of ρE(kEt

)= α (1− ψ)

(kEt /χ

)α−1. Obviously, the con-

stant pH locus is always upward sloping. Moreover, since ρE > 1, the whole constant pH

1

locus is on the right side of kEt = kE. Note that the condition for ψ in equation (9) ensures

that the constant kE locus and the constant pHt intersect at a point where pHt is positive,

which is the bubbly steady state.

Figure A-1 plots the phase diagram for{kEt , p

Ht

}. For any initial kE0 , there could be three

cases for pH0 . Point A, at which pH0 = pH0 or hE0 = hE0 , corresponds to the saddle path

equilibrium. Point B, at which pH0 < pH0 or hE0 < hE0 , corresponds to the asymptotic bubbly

equilibrium. Point C, at which hE0 > hE0 , has an explosive path of housing bubble, hence is

not sustainable.

B. Proof of Propositions and Lemmas

In this section, we prove the various lemmas and propositions.

Proof of Lemma 1. The growth rate of E-firms’output is

Y Et+1

Y Et

=Y Et+1

KEt+1

KEt+1

KEt

KEt

Y Et

=ρEt+1

(1− ψ)α

KEt+1

KEt

(1− ψ)α

ρEt, (A5)

where KEt+1/K

Et depends on the equilibrium portfolio share of entrepreneurs in physical

capital, φEt . We now solve for the equilibrium portfolio share of entrepreneurial savings in

housing. Using the housing market-clearing condition, H = HEt , we have

(1− φEt

) 1

1 + β−1ψ(KEt

)α (Atχn

Et Nt

)1−α= PH

t H. (A6)

Forwarding (A6) by one period, and with(KEt+1

)α (At+1χn

Et+1Nt+1

)1−α= KE

t+1ρEt+1/ [α (1− ψ)],

equation (A6) can be rewritten as

(1− φEt+1

) 1

1 + β−1ψρEt+1K

Et+1

α (1− ψ)= PH

t+1H. (A7)

With the law of motion for capital (9) , (A7) can be rewritten as

(1− φEt+1

) 1

1 + β−1ψρEt+1

α (1− ψ)

φEt1 + β−1

ψ(KEt

)α (Atχn

Et Nt

)1−α= PH

t+1H. (A8)

2

Dividing (A8) by (A6) for all t, we have

1− φEt+11− φEt

φEt1 + β−1

ψρEt+1α (1− ψ)

=PHt+1

PHt

= ρEt+1,

or simply

1− φEt+11− φEt

φEt1 + β−1

ψ

α (1− ψ)= 1. (A9)

Equation (A9) is a first-difference equation capturing the dynamics of φEt . One solution to

equation (A9) is that

φEt =α(1 + β−1

)(1− ψ)

ψ, ∀t. (A10)

To solve for KEt+1/K

Et , we substitute (A10) into (9) and obtain

KEt+1 = ρEt K

Et . (A11)

Equation (A11) is a variant of the no-arbitrage condition. Comparing (16) in the fundamental

equilibrium and (A11) in the bubbly equilibrium, we see that in the bubbly equilibrium the

optimal portfolio choice by an entrepreneur equalizes the return to capital investment and

the return to bubbles by crowding out E-firms’capital investment.

Finally, substituting (A11) into (A5) , we obtain Y Et+1/Y

Et = ρEt+1 = ρHt+1.�

Proof of Proposition 1. We first decompose the ratio of housing value to aggregate outputas

PHt H

Yt=PHt H

Y Et

Y Et

Y Et + Y F

t

. (A12)

The first argument on the right side of (A12) , PHt H/Y

Et , can be further expressed as

PHt H

Y Et

=PHt H

KEt+1

KEt+1

Y Et

=1− φEtφEt

KEt+1

Y Et

. (A13)

Equation (A11) implies

KEt+1 = (1− ψ)αY E

t . (A14)

With both (A10) and (A14) , it is straightforward that PHt H/Y

Et is a constant. Therefore,

3

by log-differencing (A12) , we obtain (25) .

Finally, we derive Y Et /(Y Et + Y F

t

). Using (6) , Y E

t can be expressed as

Y Et =

NEt

Nt (1− ψ)καFAtNt, (A15)

where κF ≡ kFt/ (nFtAt) = (α/R)1

1−α . Similarly, it is easy to show that

Y Et + Y F

t =

(1 +

ψ

1− ψNEt

Nt

)καFAtNt. (A16)

�Proof of Proposition 2. To prove this proposition, consider the fundamental equilibrium–

that is, φEt = 1 for all t. According to (12) , introducing housing reduces the steady-state

physical capital. Hence, we only need to show under which condition a marginal reduction

in physical capital reduces total entrepreneurial consumption. Aggregating the budget con-

straints of the young and old entrepreneurs at period t, and using the capital market-clearing

condition, we obtain

[Ntc

E1,t +Nt−1c

E1,t−1 +Nt+1k

Et+1

]/2 = Nt

[mt + ρEt k

Et

]/2. (A17)

With the definition of cEt and mt + ρEt kEt = [ψ + (1− ψ)α] yEt , a detrended version of (A17)

is

cEt = [ψ + (1− ψ)α] yEt − kEt+1(1 + z)(1 + ν). (A18)

Taking the derivative of the right side of (A18) with respect to kE at the steady state, we

can obtain the following suffi cient condition for introducing bubbles to reduce aggregate

consumption for entrepreneurs:

[ψ + (1− ψ)α]MPKE∗ |φE=1> (1 + z)(1 + ν). (A19)

With (13) and the definition of MPKE, the inequality (A19) can be rewritten as

[ψ + (1− ψ)α]α(1 + β−1

)(1 + z) (1 + ν) /ψ > (1 + z)(1 + ν). (A20)

4

Reordering (A20) , we obtain (28) .

The proof of the welfare implications for entrepreneurs in both transition and post-transition

stages is straightforward. Substituting the detrended version of (9) into (A18), we obtain

cEt =

[ψ + (1− ψ)α− ψ

α(1 + β−1

)] yEt .Since E-firms’capital increases monotonically, we need to prove only

∂cEt

∂kEt=

[ψ + (1− ψ)α− ψ

α(1 + β−1

)]MPKEt |φE=1> 0. (A21)

By assumption (28) , ∂cEt /∂kEt > 0 for all period t. Hence, housing bubbles, by crowding out

physical capital, reduce total entrepreneurial consumption.

For entrepreneurs born during the transition, (A22) becomes

log(mt − sEt

)+ β log ρEsEt

= (1 + β) log kEt + C,

where C is a function of parameters. Therefore, it is easy to see that a reduction in capital

stock would reduce the welfare of entrepreneurs born during the transition.

For the entrepreneur born in the post-transition stage, but before reaching the steady state,

the lifetime utility can be expressed as

log(mt − sEt

)+ β log ρEt+1s

Et

= log

(ψρEt k

Et

(1 + β)α (1− ψ)

)+ β log

ρEt+1kEt+1 (1 + ν)

φEt. (A22)

5

At steady state, equation (A22) , after being detrended, becomes

(1 + β) log ρE∗kE∗ − β log φE∗ + C

= (1 + β) logα1− ψψ

(1 + β−1

)φE∗

(1 + z) (1 + ν)

[ψφE∗χ1−α(

1 + β−1)

(1 + z) (1 + ν)

] 11−α

−β log φE∗ + C

=

[α (1 + β)

1− α − β]

log φE∗ + C, (A23)

where both C and C are functions of parameters. Hence, introducing housing (i.e., a re-

duction in φE∗) reduces the steady-state welfare if α(1+β)1−α > β or α

(1 + β−1

)> 1 − α.

Note that the joint participation and incentive constraints of the young entrepreneurs im-

plies m = ψyE > w = (1− α) (1− ψ) yE, which gives the following parameter restriction:

ψ > (1− α) (1− ψ), or equivalently, ψψ+α(1−ψ) > 1 − α. Therefore, with assumption (28) ,

introducing housing reduces the entrepreneurial lifetime utility at the steady state.

For entrepreneurs born during the post-transition stage, it is easy to show that equation

(A22) becomes

log(mt − sEt

)+ β log ρEt+1s

Et

= α (1 + αβ) log kEt − (1− α) β log φEt + C, (A24)

where C is a function of parameters. We would like to compare (A24) under the fundamental

and the bubbly equilibrium. In the bubbly equilibrium, since kEt is smaller due to previous

cohort’s investment in housing, a suffi cient condition for welfare loss with a reduction in φEtis

α (1 + αβ) > (1− α) β

or α(1 + β−1

)> 1− α2.�

Proof of Proposition 3: We consider the portfolio choice of an entrepreneur of age jat period t. Suppose that all other entrepreneurs alive at period t hold the same share of

savings in housing, φEk,t = φEt for k 6= j, so that the no-arbitrage condition holds,PHt+1PHt

= ρEt+1.

Accordingly, the age-j entrepreneur is indifferent between housing and physical capital. So

6

φEj,t = φEt is an equilibrium solution. The same logic applies for the portfolio choice of other

entrepreneurs alive at period t. Hence, there exists a solution that all entrepreneurs hold the

same share of housings in their net worth.�

C. Numerical Algorithm

Again, we detrend all per capita variables (except labor inputs and housing) as xt = xt/At.

For total labor inputs on both the supply and demand sides, we detrend them by dividing

them by the size of the population, Nt. Denote nEt ≡∑JE−1

j=1 nEj,t as the total detrended labor

demand by E-firms. Since the aggregation holds, the following equation determines total

labor allocated to E-firms:

nEt = [(1− ψ) (1− τ yt )χ]1α

(Rl − 1 + δ

α

) 11−α

kEt /χ. (A25)

Similarly, denote nwt ≡∑JR−1

j=1 nwj,t as the total detrended labor supply by workers. If nEt >

nwt , we have

wt = (1− ψ) (1− τ yt ) (1− α)(kEt /n

Et

)αχ1−α, (A26)

nEt = nwt , nFt = kFt = 0. (A27)

Otherwise,

wt = (1− α)

(α

Rl − 1 + δ

) α1−α

(A28)

nFt = nwt − nEt (A29)

kFt =(α/(Rl − 1 + δ

)) 11−α nFt . (A30)

7

Also, we have the following equations for both the transition and post-transition stages:

ρEt = α (1− ψ) [(1− α) (1− ψ) (1− τ yt )χ/wt]1−αα + 1− δ, (A31)

mt = ψ(1− τ yt )(kEt

)α (χnEt

)1−α/JE−1∑j=1

nEj,t, (A32)

HEt = H, (A33)

pHt = pHt+1 (1 + z) (1 + ν) /ρEt+1, (A34)

pHt H =(1− φEt

) J−1∑j=JE−1

nEj,tsEj,t, (A35)

kEt+1 = φEt

J−1∑j=JE−1

nEj,tsEj,t. (A36)

We assume transition takes T periods. At period T , the economy enters the steady state.

The algorithm to solve for the transition takes the following steps:

1. Guess the sequence of{φEt , k

Et+1, p

Ht

}T−1t=1

.

2. Given kE1 , compute{nEt , wt, n

Ft , k

Ft+1, ρ

Et , mt, s

Ej,t, s

wj,t, H

Et

}T−1t=1

.

3. Check the following conditions for each period t = 1, 2, .., T − 1:

φEt = 1− pHt H∑J−1j=JE−1 n

Ej,ts

Ej,t

, (A37)

pHt = pHt+1 (1 + z) (1 + ν) /ρEt+1, (A38)

kEt+1 = φEt

J−1∑j=JE−1

nEj,tsEj,t/ [(1 + z) (1 + ν)] , (A39)

and (since ρET+1 is not known)

kET+1

= kE∗ =

[φE∗ψ(1− τ y)χ1−α(

1 + β−1)

(1 + z) (1 + ν)

] 11−α

. (A40)

8

FigureA‐1:PhaseDiagramoftheBenchmarkEconomy

ptH

k E kt1E ( E )1[(1 z)(1 )] k E

kt1E kt

E

pt1H pt

H

kt1E

Bubbless Steady State

B

Bubbly Steady State

A

C